Find f(g(x)) f(x)=5x-1 , g(x)=x^2-2

$f (x) = 5 x - 1$ , $g (x) = x^{2} - 2$

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 $f$ .

$f (x^{2} - 2) = 5 (x^{2} - 2) - 1$

Step 3

Simplify each term.

Apply the distributive property.

$f (x^{2} - 2) = 5 x^{2} + 5 \cdot - 2 - 1$

Multiply $5$ by $- 2$ .

$f (x^{2} - 2) = 5 x^{2} - 10 - 1$

Step 4

Subtract $1$ from $- 10$ .

$f (x^{2} - 2) = 5 x^{2} - 11$