Find f(g(x)) f(x)=3x-5 g(x)=x^2+2

$f (x) = 3 x - 5$ $g (x) = x^{2} + 2$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x^{2} + 2)$ by substituting in the value of $g$ into $f$ .

$f (x^{2} + 2) = 3 (x^{2} + 2) - 5$

Step 3

Simplify each term.

Apply the distributive property.

$f (x^{2} + 2) = 3 x^{2} + 3 \cdot 2 - 5$

Multiply $3$ by $2$ .

$f (x^{2} + 2) = 3 x^{2} + 6 - 5$

Step 4

Subtract $5$ from $6$ .

$f (x^{2} + 2) = 3 x^{2} + 1$