College Algebra 1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: Jay Abramson
1 Prerequisites 2 Equations And Inequalities 3 Functions 4 Linear Functions 5 Polynomial And Rational Functions 6 Exponential And Logarithmic Functions 7 Systems Of Equations And Inequalities 8 Analytic Geometry 9 Sequences, Probability And Counting Theory Chapter3: Functions
3.1 Functions And Function Notation 3.2 Domain And Range 3.3 Rates Of Change And Behavior Of Graphs 3.4 Composition Of Functions 3.5 Transformation Of Functions 3.6 Absolute Value Functions 3.7 Inverse Functions Chapter Questions Section3.4: Composition Of Functions
Problem 1TI: Find and simplify the functions (fg)(x) and (fg)(x) . f(x)=x1 and g(x)=x21 Are they the same... Problem 2TI: The gravitational force on a planet a distance r from the sun is given by the function G(r) . The... Problem 3TI: Using Table 1, evaluate f(g(1))andg(f(4)) . Problem 4TI: Using Figure 1, evaluate g(f(2)) . Problem 5TI: Given f(t)=t2tandh(x)=3x+2 , evaluate a.h(f(2)) b.h(f(2)) Problem 6TI: Find the domain of (fg)(x) where f(x)=1x2 and g(x)=x+4 Problem 7TI: Write f(x)=434+x2 as the composition of two functions. Problem 1SE: How does one find the domain of the quotient of two functions, fg ? Problem 2SE: What is the composition of two functions, fg ? Problem 3SE: If the order is reversed when composing two functions, can the result ever be the same as the answer... Problem 4SE: How do you find the domain for the composition of two functions, fg ? Problem 5SE: For the following exercises, determine the domain for each function in interval notation 5. Given... Problem 6SE: For the following exercises, determine the domain for each function in interval notation 6. Given... Problem 7SE: For the following exercises, determine the domain for each function in interval notation 7. Given... Problem 8SE: For the following exercises, determine the domain for each function in interval notation 8. Given... Problem 9SE: For the following exercises, determine the domain for each function in interval notation 9. Given... Problem 10SE: For the following exercises, determine the domain for each function in interval notation Given... Problem 11SE: For the following exercises, determine the domain for each function in interval notation 11. For the... Problem 12SE: For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your... Problem 13SE: For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your... Problem 14SE: For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your... Problem 15SE: For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your... Problem 16SE: For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your... Problem 17SE: For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your... Problem 18SE: For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your... Problem 19SE: For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your... Problem 20SE: For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers.... Problem 21SE: For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers.... Problem 22SE: For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers.... Problem 23SE: For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers.... Problem 24SE: For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers.... Problem 25SE: For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers.... Problem 26SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 27SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 28SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 29SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 30SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 31SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 32SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 33SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 34SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 35SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 36SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 37SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 38SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 39SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 40SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 41SE: For the following exercises, find functions f(x)andg(x) so the given function can be expressed as... Problem 42SE: For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to... Problem 43SE: For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to... Problem 44SE: For the following exercises, use the graph of f, shown in Figure 4, and g, shown inFigure 5, to... Problem 45SE: For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to... Problem 46SE: For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to... Problem 47SE: For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to... Problem 48SE: For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to... Problem 49SE: For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to... Problem 50SE: For the following exercises, use the graph of f(x), shown in Figure 6,g(x), shown in Figure 7, and... Problem 51SE: For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and... Problem 52SE: For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and... Problem 53SE: For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and... Problem 54SE: For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and... Problem 55SE: For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and... Problem 56SE: For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and... Problem 57SE: For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and... Problem 58SE: For the following exercises, use the function values for f and g shown in Table 3 to evaluate each... Problem 59SE: For the following exercises, use the function values for f and g shown in Table 3 to evaluate each... Problem 60SE: For the following exercises, use the function values for f and g shown in Table 3 to evaluate each... Problem 61SE: For the following exercises, use the function values for f and g shown in Table 3 to evaluate each... Problem 62SE: For the following exercises, use the function values for f and g shown in Table 3 to evaluate each... Problem 63SE: For the following exercises, use the function values for f and g shown in Table 3 to evaluate each... Problem 64SE: For the following exercises, use the function values for f and g shown in Table 3 to evaluate each... Problem 65SE: For the following exercises, use the function values for f and g shown in Table 3 to evaluate each... Problem 66SE: For the following exercises, use the function values for f and g shown in Table 4 to evaluate each... Problem 67SE: For the following exercises, use the function values for f and g shown in Table 4 to evaluate each... Problem 68SE: For the following exercises, use the function values for f and g shown in Table 4 to evaluate each... Problem 69SE: For the following exercises, use the function values for f and g shown in Table 4 to evaluate each... Problem 70SE: For the following exercises, use the function values for f and g shown in Table 4 to evaluate each... Problem 71SE: For the following exercises, use the function values for f and g shown in Table 4 to evaluate each... Problem 72SE: For the following exercises, use each pair of functions to find f(g(0))andg(f(0)) . 72.... Problem 73SE: For the following exercises, use each pair of functions to find f(g(0))andg(f(0)) . 73.... Problem 74SE: For the following exercises, use each pair of functions to find f(g(0))andg(f(0)) . 74.... Problem 75SE: For the following exercises, use each pair of functions to find f(g(0))andg(f(0)) . 75.... Problem 76SE: For the following exercises, use the functions f(x)=2x2+1 and f(x)=3x+5 to evaluate or find the... Problem 77SE: For the following exercises, use the functions f(x)=2x2+1 and f(x)=3x+5 to evaluate or find the... Problem 78SE: For the following exercises, use the functions f(x)=2x2+1 and f(x)=3x+5 to evaluate or find the... Problem 79SE: For the following exercises, use the functions f(x)=2x2+1 and f(x)=3x+5 to evaluate or find the... Problem 80SE: For the following exercises, use f(x)=x3+1 and g(x)=x13 . Find (fg)(x) and (gf)(x) . Compare the two... Problem 81SE: For the following exercises, use f(x)=x3+1 and g(x)=x13 . Find (fg)(2) and (gf)(2) . Problem 82SE: For the following exercises, use f(x)=x3+1 and g(x)=x13 . What is the domain of (gf)(x) ? Problem 83SE: For the following exercises, use f(x)=x3+1 and g(x)=x13 . What is the domain of (fg)(x) ? Problem 84SE: For the following exercises, use f(x)=x3+1 and g(x)=x13 . Let f(x)=1x . a. Find (ff)(x) . b. Is... Problem 85SE: For the following exercises, let F(x)=(x+1)5,f(x)=x5,andg(x)=x+1 . 85. True or False: (gf)(x)=F(x) . Problem 86SE: For the following exercises, let F(x)=(x+1)5,f(x)=x5,andg(x)=x+1 . 86. True or False: (fg)(x)=F(x) . Problem 87SE: For the following exercises, Find the composition when f(x)=x2+2 for all x0 and g(x)=x2 . 87.... Problem 88SE: For the following exercises, Find the composition when f(x)=x2+2 for all x0 and g(x)=x2 . 88.... Problem 89SE: For the following exercises, Find the composition when f(x)=x2+2 for all x0 and g(x)=x2 . 89.... Problem 90SE: The function D(p) gives the number of items that will be demanded when the price is p. The... Problem 91SE: The function A(d) gives the pain level on a scale of 0 to 10 experienced by a patient with d... Problem 92SE: A store offers customers a 30% discount on the price x of selected items. Then, the store takes off... Problem 93SE: A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of... Problem 94SE: A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius... Problem 95SE: Use the function you found in the previous exercise to find the total area burned after 5 minutes. Problem 96SE: The radius r, in inches, of a spherical balloon isrelated to the volume, V, by r(V)=3V43 . Air is... Problem 97SE: The number of bacteria in a refrigerated food product is given by N(T)=23T256T+1,3T33 ,where T is... Problem 4SE: How do you find the domain for the composition of two functions, fg ?
2. Intro To Real Analysis
Transcribed Image Text: 2)
Let f and g be the functions whose values at x = R are given by
f(x)
=
1-x², and g(x) = √√x
(i)
Find (g of)(x) and (fog)(x).
(ii)
What are the domains D(g of) and D(fog)?
Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.
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