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Let f(x) = 2x - 1 and g(x) = x² + 1. Find and simplify: (g. ) ( ) Select one: A. 1 C. –2 D. -1 O E.2

Let f(x) = 2x - 1 and g(x) = x² + 1. Find and simplify: (g. ) ( ) Select one: A. 1 C. –2 D. -1 O E.2

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 Statement Let \( f(x) = 2x - 1 \) and \( g(x) = x^2 + 1 \). Find and simplify: \( (g \circ f) \left( \frac{1}{2} \right) \). ### Answer Choices Select one: - A. 1 - B. \(\frac{1}{2}\) - C. -2 - D. -1 - E. 2
Transcribed Image Text:### Problem Statement Let \( f(x) = 2x - 1 \) and \( g(x) = x^2 + 1 \). Find and simplify: \( (g \circ f) \left( \frac{1}{2} \right) \). ### Answer Choices Select one: - A. 1 - B. \(\frac{1}{2}\) - C. -2 - D. -1 - E. 2
### Functions and Composition: Practice Problem Consider the functions: \[ f(x) = x^2 + 3x - 2 \] \[ g(x) = \sqrt{x + 1} \] We are asked to find and simplify the composition of functions \((f \circ g)(x)\) evaluated at \(x = 3\). ### Problem: Find and simplify: \((f \circ g)(3)\) #### Select one: - A. \(-8\) - B. 6 - C. 8 - D. 4 - E. \(-6\) ### Steps to Solve: 1. **Evaluate \(g(3)\):** \[ g(x) = \sqrt{x + 1} \] Substitute \(x = 3\): \[ g(3) = \sqrt{3 + 1} = \sqrt{4} = 2 \] 2. **Substitute \(g(3)\) into \(f(x)\):** \[ f(x) = x^2 + 3x - 2 \] Substitute \(x = 2\): \[ f(2) = 2^2 + 3 \cdot 2 - 2 = 4 + 6 - 2 = 8 \] Thus, the correct answer is: - C. 8
Transcribed Image Text:### Functions and Composition: Practice Problem Consider the functions: \[ f(x) = x^2 + 3x - 2 \] \[ g(x) = \sqrt{x + 1} \] We are asked to find and simplify the composition of functions \((f \circ g)(x)\) evaluated at \(x = 3\). ### Problem: Find and simplify: \((f \circ g)(3)\) #### Select one: - A. \(-8\) - B. 6 - C. 8 - D. 4 - E. \(-6\) ### Steps to Solve: 1. **Evaluate \(g(3)\):** \[ g(x) = \sqrt{x + 1} \] Substitute \(x = 3\): \[ g(3) = \sqrt{3 + 1} = \sqrt{4} = 2 \] 2. **Substitute \(g(3)\) into \(f(x)\):** \[ f(x) = x^2 + 3x - 2 \] Substitute \(x = 2\): \[ f(2) = 2^2 + 3 \cdot 2 - 2 = 4 + 6 - 2 = 8 \] Thus, the correct answer is: - C. 8
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