Solve the Function Operation m(x) = square root of x+2 , n(x)=x-3 , (m*n)(x) =

$m (x) = \sqrt{x + 2}$ , $n (x) = x - 3$ , $(m \cdot n) (x)$

Step 1

Evaluate $m \cdot n$ .

Replace the function designators in $m \cdot n$ with the actual functions.

$(\sqrt{x + 2}) \cdot (x - 3)$

Apply the distributive property.

$\sqrt{x + 2} x + \sqrt{x + 2} \cdot - 3$

Move $- 3$ to the left of $\sqrt{x + 2}$ .

$\sqrt{x + 2} x - 3 \sqrt{x + 2}$

Step 2

Evaluate $m \cdot n$ at $x$ .

$\sqrt{(x) + 2} (x) - 3 \sqrt{(x) + 2}$

Step 3

Simplify $\sqrt{(x) + 2} (x) - 3 \sqrt{(x) + 2}$ .

Remove parentheses.

$\sqrt{(x) + 2} (x) - 3 \sqrt{(x) + 2}$

Remove parentheses.

$\sqrt{x + 2} x - 3 \sqrt{x + 2}$