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19. If ƒ(x)=3x²-15 and g(x)-1-3, find (S-2X-6). A. 57 B. 60 C. -48

19. If ƒ(x)=3x²-15 and g(x)-1-3, find (S-2X-6). A. 57 B. 60 C. -48

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 19: **Given:** \( f(x) = 3x^2 - 15 \) \( g(x) = 1 - \frac{2}{3}x \) **Task:** Find \( (f \circ g)(x) \) evaluated at \( x = 6 \). **Choices:** - A. 57 - B. 60 - C. -48 - D. -61 - E. All of the Above - F. None of the Above **Solution Explanation:** 1. **Compute \( g(6) \):** \[ g(x) = 1 - \frac{2}{3} \times x \] Substitute \( x = 6 \): \[ g(6) = 1 - \frac{2}{3} \times 6 = 1 - 4 = -3 \] 2. **Compute \( f(g(6)) = f(-3) \):** \[ f(x) = 3x^2 - 15 \] Substitute \( x = -3 \): \[ f(-3) = 3(-3)^2 - 15 = 3 \times 9 - 15 = 27 - 15 = 12 \] Therefore, the correct answer is **not listed as a choice** under options A to D, and does not fit the criteria for E. **Answer:** F. None of the Above
Transcribed Image Text:### Problem 19: **Given:** \( f(x) = 3x^2 - 15 \) \( g(x) = 1 - \frac{2}{3}x \) **Task:** Find \( (f \circ g)(x) \) evaluated at \( x = 6 \). **Choices:** - A. 57 - B. 60 - C. -48 - D. -61 - E. All of the Above - F. None of the Above **Solution Explanation:** 1. **Compute \( g(6) \):** \[ g(x) = 1 - \frac{2}{3} \times x \] Substitute \( x = 6 \): \[ g(6) = 1 - \frac{2}{3} \times 6 = 1 - 4 = -3 \] 2. **Compute \( f(g(6)) = f(-3) \):** \[ f(x) = 3x^2 - 15 \] Substitute \( x = -3 \): \[ f(-3) = 3(-3)^2 - 15 = 3 \times 9 - 15 = 27 - 15 = 12 \] Therefore, the correct answer is **not listed as a choice** under options A to D, and does not fit the criteria for E. **Answer:** F. None of the Above
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Step 1: Given value of f(x) and g(x)

Given, f left parenthesis x right parenthesis equals 3 x squared minus 15 comma space space space g left parenthesis x right parenthesis equals 1 minus 2 over 3 x

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