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ven the graphs of f(z) and g(z) below, find the composition of functions f(g(4)). lect the correct answer below: f(g(4)) = -3 f(g(4))--4 f(g(4)) = -2 f(g(4))--1 f(g(4)) - 1 4 UT IN g(x) 4 f(x)

ven the graphs of f(z) and g(z) below, find the composition of functions f(g(4)). lect the correct answer below: f(g(4)) = -3 f(g(4))--4 f(g(4)) = -2 f(g(4))--1 f(g(4)) - 1 4 UT IN g(x) 4 f(x)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** Given the graphs of \( f(x) \) and \( g(x) \) below, find the composition of functions \( f(g(4)) \). **Graph Explanation:** The graph provided consists of two functions, \( f(x) \) and \( g(x) \): - The blue curve represents \( f(x) \), which appears to be a parabola opening upwards. - The red curve represents \( g(x) \), which appears to be a parabola opening downwards. **Axes Details:** - The horizontal axis (x-axis) ranges from \(-5\) to \(7\). - The vertical axis (y-axis) ranges from \(-3\) to \(6\). **Points of Interest:** To solve for \( f(g(4)) \): 1. Locate the value of \( g(4) \) on the graph: - Find \( x = 4 \) on the horizontal axis. - Trace upwards to the red curve, \( g(x) \), to find the corresponding \( y \)-coordinate. - From the graph, \( g(4) = 2 \). 2. Use the value of \( g(4) = 2 \) to find \( f(2) \): - Locate \( x = 2 \) on the horizontal axis. - Trace upwards to the blue curve, \( f(x) \), to find the corresponding \( y \)-coordinate. - From the graph, \( f(2) = -2 \). **Solution:** Given the steps above, \( f(g(4)) = f(2) = -2 \). **Options:** Select the correct answer below: - ⬜ \( f(g(4)) = -3 \) - ⬜ \( f(g(4)) = -4 \) - ✅ \( f(g(4)) = -2 \) - ⬜ \( f(g(4)) = -1 \) - ⬜ \( f(g(4)) = 1 \)
Transcribed Image Text:**Problem Statement:** Given the graphs of \( f(x) \) and \( g(x) \) below, find the composition of functions \( f(g(4)) \). **Graph Explanation:** The graph provided consists of two functions, \( f(x) \) and \( g(x) \): - The blue curve represents \( f(x) \), which appears to be a parabola opening upwards. - The red curve represents \( g(x) \), which appears to be a parabola opening downwards. **Axes Details:** - The horizontal axis (x-axis) ranges from \(-5\) to \(7\). - The vertical axis (y-axis) ranges from \(-3\) to \(6\). **Points of Interest:** To solve for \( f(g(4)) \): 1. Locate the value of \( g(4) \) on the graph: - Find \( x = 4 \) on the horizontal axis. - Trace upwards to the red curve, \( g(x) \), to find the corresponding \( y \)-coordinate. - From the graph, \( g(4) = 2 \). 2. Use the value of \( g(4) = 2 \) to find \( f(2) \): - Locate \( x = 2 \) on the horizontal axis. - Trace upwards to the blue curve, \( f(x) \), to find the corresponding \( y \)-coordinate. - From the graph, \( f(2) = -2 \). **Solution:** Given the steps above, \( f(g(4)) = f(2) = -2 \). **Options:** Select the correct answer below: - ⬜ \( f(g(4)) = -3 \) - ⬜ \( f(g(4)) = -4 \) - ✅ \( f(g(4)) = -2 \) - ⬜ \( f(g(4)) = -1 \) - ⬜ \( f(g(4)) = 1 \)
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