QuestionCalculate $f(g(12))$ and $g(f(12))$ for $f(x)=14x+2$ and $g(x)=\sqrt{x-7}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as $f(x) =14x +$ . The function $g(x)$ is defined as $g(x) = \sqrt{x -7}$
3. We are asked to find the values of $f(g(12))$ and $g(f(12))$

STEP 2

First, we need to find the value of $g(12)$ . We can do this by substituting $12$ into the function $g(x)$ .
$g(12) = \sqrt{12 -7}$

STEP 3

Calculate the value of $g(12)$ .
$g(12) = \sqrt{12 -7} = \sqrt{5}$

STEP 4

Now that we have the value of $g(12)$ , we can substitute this into the function $f(x)$ to find the value of $f(g(12))$ .
$f(g(12)) = f(\sqrt{}) =14\sqrt{} +2$

STEP 5

Now, we need to find the value of $f(12)$ . We can do this by substituting $12$ into the function $f(x)$ .
$f(12) =14 \cdot12 +2$

STEP 6

Calculate the value of $f(12)$ .
$f(12) =14 \cdot12 +2 =170$

STEP 7

Now that we have the value of $f(12)$ , we can substitute this into the function $g(x)$ to find the value of $g(f(12))$ .
$g(f(12)) = g(170) = \sqrt{170 -7}$

STEP 8

Calculate the value of $g(f(12))$ .
$g(f(12)) = \sqrt{170 -7} = \sqrt{163}$ So, the values of $f(g(12))$ and $g(f(12))$ are $14\sqrt{5} +2$ and $\sqrt{163}$ respectively.

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