QuestionFind $f(g(x))$ and $g(f(x))$ and determine whether the pair of functions $f$ and $g$ are inverses of each other. $f(x)=8 x+3 \text { and } g(x)=\frac{x-3}{8}$ a. $f(g(x))=$ $\square$ (Simplify your answer.)

Studdy Solution

STEP 1

1. We are given two functions $f(x) = 8x + 3$ and $g(x) = \frac{x-3}{8}$ .
2. To determine if two functions are inverses, we need to check if $f(g(x)) = x$ and $g(f(x)) = x$ .

STEP 2

1. Compute $f(g(x))$ .
2. Simplify $f(g(x))$ .
3. Compute $g(f(x))$ .
4. Simplify $g(f(x))$ .
5. Determine if $f$ and $g$ are inverses by checking if both compositions equal $x$ .

STEP 3

Substitute $g(x)$ into $f(x)$ to find $f(g(x))$ .
Given: $f(x) = 8x + 3$ $g(x) = \frac{x-3}{8}$
Substitute $g(x)$ into $f(x)$ : $f(g(x)) = f\left(\frac{x-3}{8}\right)$

STEP 4

Simplify $f(g(x))$ .
$f\left(\frac{x-3}{8}\right) = 8\left(\frac{x-3}{8}\right) + 3$
Distribute the 8: $= x - 3 + 3$
Simplify: $= x$
The simplified expression for $f(g(x))$ is $\boxed{x}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms