Let f(x) = 2x - 1 and g(x) = x2 + x - 2. Find the function: (f/g)(x).

Name: Let f(x) = 2x - 1 and g(x) = x2 + x - 2. Find the function: (f/g)(x).
Uploaded: 2024-03-20T06:47:22.000Z
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Description: Let f(x) = 2x - 1 and g(x) = x2 + x - 2. Find the function: (f/g)(x).

Given:fx=2x-1gx=x2+x-2Formula:fgx=fxgx

Answered: Let f(x) = 2x - 1 and g(x) = x2 + x -…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.7: Inverse Functions

Problem 2SE: Why do we restrict the domain of the function f(x)=x2 to find the function's inverse?

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Let f(x) = 2x - 1 and g(x) = x² + x - 2. Find the function: (f/g)(x).

Expert Solution

Step 1 Let us find the value of given function

$G i v e n : f (x) = 2 x - 1 g (x) = x^{2} + x - 2 F o r m u l a : \frac{f}{g} (x) = \frac{f (x)}{g (x)}$

Step 2

$= \frac{f (x)}{g (x)} = \frac{2 x - 1}{x^{2} + x - 2} = \frac{2 x - 1}{x^{2} + 2 x - x - 2} \frac{f}{g} (x) = \frac{2 x - 1}{(x + 2) (x - 1)}$

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