Find f(g(x)) f(x)=2x-5 , g(x)=2x^2-4

$f (x) = 2 x - 5$ , $g (x) = 2 x^{2} - 4$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $- 4$ .

$f (2 x^{2} - 4) = 4 x^{2} - 8 - 5$

Step 4

Subtract $5$ from $- 8$ .

$f (2 x^{2} - 4) = 4 x^{2} - 13$