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1 X+8 and h(«) = x- = 12) If what is the value of g(h(- 8))? 1) 0 2) 9 3) 5 4) 4

1 X+8 and h(«) = x- = 12) If what is the value of g(h(- 8))? 1) 0 2) 9 3) 5 4) 4

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Educational Content on Function Problems #### Question 12 If \( g(x) = \frac{1}{2}x + 8 \) and \( h(x) = \frac{1}{2}x - 2 \), what is the value of \( g(h(-3)) \)? Options: 1. 0 2. 9 3. 5 4. 4 #### Question 13 If \( f(x) = x + 1 \) and \( g(x) = x^2 - 1 \), the expression \( (g \circ f)(x) \) equals 0 when \( x \) is equal to: Options: 1. 1 and -1 2. 0, only 3. -2, only 4. 0 and -2 #### Question 14 If \( f(x) = \frac{2}{\sqrt{5-x^2}} \) and \( g(x) = x + 1 \), evaluate \( (f \circ g)(0) \). #### Question 15 If \( f(x) = x^2 - 6 \) and \( g(x) = 2^x - 1 \), determine the value of \( (g \circ f)(-3) \). ### Explanation of the Questions These questions involve the composition of functions, which is a fundamental concept in mathematics. They require understanding of how to substitute one function into another and solve for specific conditions or values. The goal is to evaluate or determine the function outputs correctly using algebraic manipulation and substitution.
Transcribed Image Text:### Educational Content on Function Problems #### Question 12 If \( g(x) = \frac{1}{2}x + 8 \) and \( h(x) = \frac{1}{2}x - 2 \), what is the value of \( g(h(-3)) \)? Options: 1. 0 2. 9 3. 5 4. 4 #### Question 13 If \( f(x) = x + 1 \) and \( g(x) = x^2 - 1 \), the expression \( (g \circ f)(x) \) equals 0 when \( x \) is equal to: Options: 1. 1 and -1 2. 0, only 3. -2, only 4. 0 and -2 #### Question 14 If \( f(x) = \frac{2}{\sqrt{5-x^2}} \) and \( g(x) = x + 1 \), evaluate \( (f \circ g)(0) \). #### Question 15 If \( f(x) = x^2 - 6 \) and \( g(x) = 2^x - 1 \), determine the value of \( (g \circ f)(-3) \). ### Explanation of the Questions These questions involve the composition of functions, which is a fundamental concept in mathematics. They require understanding of how to substitute one function into another and solve for specific conditions or values. The goal is to evaluate or determine the function outputs correctly using algebraic manipulation and substitution.
### Questions for Practice #### Question 8 If \( f(x) = x - 3 \) and \( g(x) = x^3 \), find \( f(g(3)) \). 1) 0 2) 6 3) 24 4) 30 #### Question 9 If \( f(x) = 4x - x^2 \) and \( g(x) = \frac{1}{x} \), then \( (f \circ g) \left(\frac{1}{2}\right) \) is equal to 1) \(\frac{4}{7}\) 2) \(-2\) 3) \(\frac{7}{2}\) 4) 4 #### Question 10 The accompanying tables define functions \( f \) and \( g \). What is \( (g \circ f)(3) \)? | \( x \) | 1 | 2 | 3 | 4 | 5 | |---------|---|---|---|---|---| | \( f(x) \) | 3 | 4 | 5 | 6 | 7 | | \( x \) | 3 | 4 | 5 | 6 | 7 | |---------|---|---|---|---|---| | \( g(x) \) | 4 | 6 | 8 | 10 | 12 | 1) 6 2) 2 3) 0 4) 4 #### Question 11 The accompanying graph is a sketch of the function \( y = f(x) \) over the interval \( 0 \le x \le 7 \). - The graph shows a sinusoidal curve with labeled points at various coordinates. What is the value of \( (f \circ f)(6) \)? 1) 1 2) 2 3) 0 4) \(-2\)
Transcribed Image Text:### Questions for Practice #### Question 8 If \( f(x) = x - 3 \) and \( g(x) = x^3 \), find \( f(g(3)) \). 1) 0 2) 6 3) 24 4) 30 #### Question 9 If \( f(x) = 4x - x^2 \) and \( g(x) = \frac{1}{x} \), then \( (f \circ g) \left(\frac{1}{2}\right) \) is equal to 1) \(\frac{4}{7}\) 2) \(-2\) 3) \(\frac{7}{2}\) 4) 4 #### Question 10 The accompanying tables define functions \( f \) and \( g \). What is \( (g \circ f)(3) \)? | \( x \) | 1 | 2 | 3 | 4 | 5 | |---------|---|---|---|---|---| | \( f(x) \) | 3 | 4 | 5 | 6 | 7 | | \( x \) | 3 | 4 | 5 | 6 | 7 | |---------|---|---|---|---|---| | \( g(x) \) | 4 | 6 | 8 | 10 | 12 | 1) 6 2) 2 3) 0 4) 4 #### Question 11 The accompanying graph is a sketch of the function \( y = f(x) \) over the interval \( 0 \le x \le 7 \). - The graph shows a sinusoidal curve with labeled points at various coordinates. What is the value of \( (f \circ f)(6) \)? 1) 1 2) 2 3) 0 4) \(-2\)
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