Find f(g(x)) f(x)=2x-5 and g(x)=x^2-2

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 2$ .

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

Step 4

Subtract $5$ from $- 4$ .

$f (x^{2} - 2) = 2 x^{2} - 9$