Solve the Function Operation m(x) = square root of x+4 , n(x)=x+3 , (m*n)(x) =

$m (x) = \sqrt{x + 4}$ , $n (x) = x + 3$ , $(m \cdot n) (x)$

Step 1

Evaluate $m \cdot n$ .

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

$(\sqrt{x + 4}) \cdot (x + 3)$

Apply the distributive property.

$\sqrt{x + 4} x + \sqrt{x + 4} \cdot 3$

Move $3$ to the left of $\sqrt{x + 4}$ .

$\sqrt{x + 4} x + 3 \sqrt{x + 4}$

Step 2

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

$\sqrt{(x) + 4} (x) + 3 \sqrt{(x) + 4}$

Step 3

Simplify $\sqrt{(x) + 4} (x) + 3 \sqrt{(x) + 4}$ .

Remove parentheses.

$\sqrt{(x) + 4} (x) + 3 \sqrt{(x) + 4}$

Remove parentheses.

$\sqrt{x + 4} x + 3 \sqrt{x + 4}$