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If f(x) = √√7 - 4x, find a formula for f-¹(x).

If f(x) = √√7 - 4x, find a formula for f-¹(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:** If \( f(x) = \sqrt{7 - 4x} \), find a formula for \( f^{-1}(x) \). **Solution Approach:** 1. Start by replacing \( f(x) \) with \( y \) for simplicity: \[ y = \sqrt{7 - 4x} \] 2. Solve for \( x \) in terms of \( y \): - Square both sides to remove the square root: \[ y^2 = 7 - 4x \] - Rearrange to solve for \( x \): \[ 4x = 7 - y^2 \] \[ x = \frac{7 - y^2}{4} \] 3. Interchange \( x \) and \( y \) to find \( f^{-1}(x) \): \[ y = \frac{7 - x^2}{4} \] Thus, the inverse function is: \[ f^{-1}(x) = \frac{7 - x^2}{4} \]
Transcribed Image Text:**Problem Statement:** If \( f(x) = \sqrt{7 - 4x} \), find a formula for \( f^{-1}(x) \). **Solution Approach:** 1. Start by replacing \( f(x) \) with \( y \) for simplicity: \[ y = \sqrt{7 - 4x} \] 2. Solve for \( x \) in terms of \( y \): - Square both sides to remove the square root: \[ y^2 = 7 - 4x \] - Rearrange to solve for \( x \): \[ 4x = 7 - y^2 \] \[ x = \frac{7 - y^2}{4} \] 3. Interchange \( x \) and \( y \) to find \( f^{-1}(x) \): \[ y = \frac{7 - x^2}{4} \] Thus, the inverse function is: \[ f^{-1}(x) = \frac{7 - x^2}{4} \]
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