f(x)=2 x+4, g(x)=(1)/(2) x-2

Name: Problem 95, Chapter 6: A Graphical Approach to Precalculus with Limits
Uploaded: 2020-08-19T00:13:21-08:00
Duration: 1 min 8 s
Channel: Heather Zimmers
Description: f(x)=2 x+4, g(x)=(1)/(2) x-2

step 1 Okay, here we have F of X and we have G of X and we're going to determine if they're inverses. A

Question

$$f(x)=2 x+4, \quad g(x)=\frac{1}{2} x-2$$

   $$f(x)=2 x+4, \quad g(x)=\frac{1}{2} x-2$$

A Graphical Approach to Precalculus with Limits

John Hornsby,… 7th Edition

Chapter 6, Problem 95

Instant Answer

Solved by Expert Heather Zimmers

08/19/2020

Step 1

Here, $g(x)$ is the inside function and $f(x)$ is the outside function. So, we substitute $g(x)$ into $f(x)$: \[f(g(x)) = 2(g(x)) + 4 = 2\left(\frac{1}{2}x - 2\right) + 4.\] Show more…

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$$f(x)=2 x+4, \quad g(x)=\frac{1}{2} x-2$$

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Key Concepts

Inverse Functions

An inverse function essentially reverses the operation of the original function, meaning that if you apply a function and then its inverse, you will retrieve the original input value. For linear functions, finding the inverse involves solving the equation y = mx + b for x and expressing x as a function of y, which provides the inverse function in its own slope-intercept form.

Linear Functions

A linear function is a function whose graph is a straight line, typically expressed in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. Linear functions are characterized by a constant rate of change, meaning that the ratio of the change in the output value to the change in the input value remains fixed across the domain.

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