Find f(g(x)) f(x)=-3x+1 g(x)=3x^2+4x-15

$f (x) = - 3 x + 1$ $g (x) = 3 x^{2} + 4 x - 15$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (3 x^{2} + 4 x - 15)$ by substituting in the value of $g$ into $f$ .

$f (3 x^{2} + 4 x - 15) = - 3 (3 x^{2} + 4 x - 15) + 1$

Step 3

Simplify each term.

Apply the distributive property.

$f (3 x^{2} + 4 x - 15) = - 3 (3 x^{2}) - 3 (4 x) - 3 \cdot - 15 + 1$

Simplify.

Multiply $3$ by $- 3$ .

$f (3 x^{2} + 4 x - 15) = - 9 x^{2} - 3 (4 x) - 3 \cdot - 15 + 1$

Multiply $4$ by $- 3$ .

$f (3 x^{2} + 4 x - 15) = - 9 x^{2} - 12 x - 3 \cdot - 15 + 1$

Multiply $- 3$ by $- 15$ .

$f (3 x^{2} + 4 x - 15) = - 9 x^{2} - 12 x + 45 + 1$

Step 4

Add $45$ and $1$ .

$f (3 x^{2} + 4 x - 15) = - 9 x^{2} - 12 x + 46$