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**Question 6 (1 point)** Given the functions \( f \) and \( g \) are defined as \( f(a) = 3a - 5 \) and \( g(a) = 2a^2 + 3 \). What is the value of \( f(g(a)) \)? - a) \( 5a^2 + 4 \) - b) \( 18a^2 - 47 \) - c) \( 18a^2 - 60a + 53 \) - d) \( 6a^2 + 4 \) - e) \( 18a^2 + 53 \) **Explanation:** This question involves function composition where you need to substitute the function \( g(a) \) into the function \( f(a) \). Calculate \( f(g(a)) \) by replacing \( a \) in \( f(a) = 3a - 5 \) with \( g(a) = 2a^2 + 3 \). 1. Substitute \( g(a) \) into \( f(a) \): \[ f(g(a)) = f(2a^2 + 3) = 3(2a^2 + 3) - 5 \] 2. Simplify: \[ f(g(a)) = 3 \times 2a^2 + 3 \times 3 - 5 \] \[ f(g(a)) = 6a^2 + 9 - 5 \] \[ f(g(a)) = 6a^2 + 4 \] Thus, the correct answer is: - d) \( 6a^2 + 4 \)

**Question 6 (1 point)** Given the functions \( f \) and \( g \) are defined as \( f(a) = 3a - 5 \) and \( g(a) = 2a^2 + 3 \). What is the value of \( f(g(a)) \)? - a) \( 5a^2 + 4 \) - b) \( 18a^2 - 47 \) - c) \( 18a^2 - 60a + 53 \) - d) \( 6a^2 + 4 \) - e) \( 18a^2 + 53 \) **Explanation:** This question involves function composition where you need to substitute the function \( g(a) \) into the function \( f(a) \). Calculate \( f(g(a)) \) by replacing \( a \) in \( f(a) = 3a - 5 \) with \( g(a) = 2a^2 + 3 \). 1. Substitute \( g(a) \) into \( f(a) \): \[ f(g(a)) = f(2a^2 + 3) = 3(2a^2 + 3) - 5 \] 2. Simplify: \[ f(g(a)) = 3 \times 2a^2 + 3 \times 3 - 5 \] \[ f(g(a)) = 6a^2 + 9 - 5 \] \[ f(g(a)) = 6a^2 + 4 \] Thus, the correct answer is: - d) \( 6a^2 + 4 \)

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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**Question 6 (1 point)** Given the functions \( f \) and \( g \) are defined as \( f(a) = 3a - 5 \) and \( g(a) = 2a^2 + 3 \). What is the value of \( f(g(a)) \)? - a) \( 5a^2 + 4 \) - b) \( 18a^2 - 47 \) - c) \( 18a^2 - 60a + 53 \) - d) \( 6a^2 + 4 \) - e) \( 18a^2 + 53 \) **Explanation:** This question involves function composition where you need to substitute the function \( g(a) \) into the function \( f(a) \). Calculate \( f(g(a)) \) by replacing \( a \) in \( f(a) = 3a - 5 \) with \( g(a) = 2a^2 + 3 \). 1. Substitute \( g(a) \) into \( f(a) \): \[ f(g(a)) = f(2a^2 + 3) = 3(2a^2 + 3) - 5 \] 2. Simplify: \[ f(g(a)) = 3 \times 2a^2 + 3 \times 3 - 5 \] \[ f(g(a)) = 6a^2 + 9 - 5 \] \[ f(g(a)) = 6a^2 + 4 \] Thus, the correct answer is: - d) \( 6a^2 + 4 \)
Transcribed Image Text:**Question 6 (1 point)** Given the functions \( f \) and \( g \) are defined as \( f(a) = 3a - 5 \) and \( g(a) = 2a^2 + 3 \). What is the value of \( f(g(a)) \)? - a) \( 5a^2 + 4 \) - b) \( 18a^2 - 47 \) - c) \( 18a^2 - 60a + 53 \) - d) \( 6a^2 + 4 \) - e) \( 18a^2 + 53 \) **Explanation:** This question involves function composition where you need to substitute the function \( g(a) \) into the function \( f(a) \). Calculate \( f(g(a)) \) by replacing \( a \) in \( f(a) = 3a - 5 \) with \( g(a) = 2a^2 + 3 \). 1. Substitute \( g(a) \) into \( f(a) \): \[ f(g(a)) = f(2a^2 + 3) = 3(2a^2 + 3) - 5 \] 2. Simplify: \[ f(g(a)) = 3 \times 2a^2 + 3 \times 3 - 5 \] \[ f(g(a)) = 6a^2 + 9 - 5 \] \[ f(g(a)) = 6a^2 + 4 \] Thus, the correct answer is: - d) \( 6a^2 + 4 \)
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