QuestionA. $(\mathrm{f}-\mathrm{g})(12)=\sqrt{12-3}-12^{2}+12$

Studdy Solution

STEP 1

Assumptions
1. The function $f(x)$ is defined as $f(x)=\sqrt{x-3}$ .
2. The function $g(x)$ is defined as $g(x)=x^{2}-x$ .
3. We are asked to find and simplify the expression $(f-g)(12)$ .

STEP 2

First, we need to evaluate the function $f(x)$ at $x=12$ .
$f(12) = \sqrt{12-3}$

STEP 3

Simplify the expression inside the square root.
$f(12) = \sqrt{9}$

STEP 4

Calculate the square root.
$f(12) = 3$

STEP 5

Now, we need to evaluate the function $g(x)$ at $x=12$ .
$g(12) = 12^{2} - 12$

STEP 6

Calculate the square of 12.
$g(12) = 144 - 12$

STEP 7

Subtract 12 from 144.
$g(12) = 132$

STEP 8

Now that we have both $f(12)$ and $g(12)$ , we can find the expression $(f-g)(12)$ by subtracting $g(12)$ from $f(12)$ .
$(f-g)(12) = f(12) - g(12)$

STEP 9

Plug in the values for $f(12)$ and $g(12)$ to calculate the expression.
$(f-g)(12) = 3 - 132$

STEP 10

Subtract 132 from 3.
$(f-g)(12) = -129$
The expression $(f-g)(12)$ simplifies to $-129$ . Therefore, the correct choice is A, and the answer is $-129$ .
A. $(\mathrm{f}-\mathrm{g})(12)=-129$ (Simplify your answer.)

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