Find f(h(x)) f(x)=3x+5 g(x)=4x^2-2 h(x)=x^2-3x+1

$f (x) = 3 x + 5$ $g (x) = 4 x^{2} - 2$ $h (x) = x^{2} - 3 x + 1$

Set up the composite result function.

$f (h (x))$

Evaluate $f (x^{2} - 3 x + 1)$ by substituting in the value of $h$ into $f$ .

$f (x^{2} - 3 x + 1) = 3 (x^{2} - 3 x + 1) + 5$

Simplify each term.

Apply the distributive property.

$f (x^{2} - 3 x + 1) = 3 x^{2} + 3 (- 3 x) + 3 \cdot 1 + 5$

Simplify.

Multiply $- 3$ by $3$ .

$f (x^{2} - 3 x + 1) = 3 x^{2} - 9 x + 3 \cdot 1 + 5$

Multiply $3$ by $1$ .

$f (x^{2} - 3 x + 1) = 3 x^{2} - 9 x + 3 + 5$

Add $3$ and $5$ .

$f (x^{2} - 3 x + 1) = 3 x^{2} - 9 x + 8$