Find f(g(x)) f(x)=5x-15 g(x)=2x^2+4x-3

$f (x) = 5 x - 15$ $g (x) = 2 x^{2} + 4 x - 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (2 x^{2} + 4 x - 3) = 5 (2 x^{2} + 4 x - 3) - 15$

Step 3

Simplify each term.

Apply the distributive property.

$f (2 x^{2} + 4 x - 3) = 5 (2 x^{2}) + 5 (4 x) + 5 \cdot - 3 - 15$

Simplify.

Multiply $2$ by $5$ .

$f (2 x^{2} + 4 x - 3) = 10 x^{2} + 5 (4 x) + 5 \cdot - 3 - 15$

Multiply $4$ by $5$ .

$f (2 x^{2} + 4 x - 3) = 10 x^{2} + 20 x + 5 \cdot - 3 - 15$

Multiply $5$ by $- 3$ .

$f (2 x^{2} + 4 x - 3) = 10 x^{2} + 20 x - 15 - 15$

Step 4

Subtract $15$ from $- 15$ .

$f (2 x^{2} + 4 x - 3) = 10 x^{2} + 20 x - 30$