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**Problem:** Given the functions \( f \) and \( g \) are defined as \[ f(a) = 3a - 5 \] and \[ g(a) = 2a^2 + 3. \] What is the value of \( f(g(a)) \)? **Options:** - a) \( 5a^2 + 4 \) - b) \( 18a^2 - 47 \) - c) \( 18a^2 - 60a + 53 \) - d) \( 6a^2 + 4 \) - e) \( 18a^2 + 53 \) **Solution Explanation:** To find the composition \( f(g(a)) \), substitute \( g(a) = 2a^2 + 3 \) into \( f(a) \). 1. Calculate \( f(g(a)) \): \[ f(g(a)) = f(2a^2 + 3) = 3(2a^2 + 3) - 5. \] 2. Simplify the expression: \[ = 6a^2 + 9 - 5, \] \[ = 6a^2 + 4. \] Therefore, the correct answer is option **d) \( 6a^2 + 4 \)**.

**Problem:** Given the functions \( f \) and \( g \) are defined as \[ f(a) = 3a - 5 \] and \[ g(a) = 2a^2 + 3. \] What is the value of \( f(g(a)) \)? **Options:** - a) \( 5a^2 + 4 \) - b) \( 18a^2 - 47 \) - c) \( 18a^2 - 60a + 53 \) - d) \( 6a^2 + 4 \) - e) \( 18a^2 + 53 \) **Solution Explanation:** To find the composition \( f(g(a)) \), substitute \( g(a) = 2a^2 + 3 \) into \( f(a) \). 1. Calculate \( f(g(a)) \): \[ f(g(a)) = f(2a^2 + 3) = 3(2a^2 + 3) - 5. \] 2. Simplify the expression: \[ = 6a^2 + 9 - 5, \] \[ = 6a^2 + 4. \] Therefore, the correct answer is option **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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**Problem:** Given the functions \( f \) and \( g \) are defined as \[ f(a) = 3a - 5 \] and \[ g(a) = 2a^2 + 3. \] What is the value of \( f(g(a)) \)? **Options:** - a) \( 5a^2 + 4 \) - b) \( 18a^2 - 47 \) - c) \( 18a^2 - 60a + 53 \) - d) \( 6a^2 + 4 \) - e) \( 18a^2 + 53 \) **Solution Explanation:** To find the composition \( f(g(a)) \), substitute \( g(a) = 2a^2 + 3 \) into \( f(a) \). 1. Calculate \( f(g(a)) \): \[ f(g(a)) = f(2a^2 + 3) = 3(2a^2 + 3) - 5. \] 2. Simplify the expression: \[ = 6a^2 + 9 - 5, \] \[ = 6a^2 + 4. \] Therefore, the correct answer is option **d) \( 6a^2 + 4 \)**.
Transcribed Image Text:**Problem:** Given the functions \( f \) and \( g \) are defined as \[ f(a) = 3a - 5 \] and \[ g(a) = 2a^2 + 3. \] What is the value of \( f(g(a)) \)? **Options:** - a) \( 5a^2 + 4 \) - b) \( 18a^2 - 47 \) - c) \( 18a^2 - 60a + 53 \) - d) \( 6a^2 + 4 \) - e) \( 18a^2 + 53 \) **Solution Explanation:** To find the composition \( f(g(a)) \), substitute \( g(a) = 2a^2 + 3 \) into \( f(a) \). 1. Calculate \( f(g(a)) \): \[ f(g(a)) = f(2a^2 + 3) = 3(2a^2 + 3) - 5. \] 2. Simplify the expression: \[ = 6a^2 + 9 - 5, \] \[ = 6a^2 + 4. \] Therefore, the correct answer is option **d) \( 6a^2 + 4 \)**.
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