Find f(g(x)) f(x)=2x-4 and g(x)=2x^2-1

$f (x) = 2 x - 4$ and $g (x) = 2 x^{2} - 1$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $- 1$ .

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

Step 4

Subtract $4$ from $- 2$ .

$f (2 x^{2} - 1) = 4 x^{2} - 6$