Find f(g(x)) f(x)=3x+2 , g(x)=2x^2-1

$f (x) = 3 x + 2$ , $g (x) = 2 x^{2} - 1$

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 $f$ .

$f (2 x^{2} - 1) = 3 (2 x^{2} - 1) + 2$

Step 3

Simplify each term.

Apply the distributive property.

$f (2 x^{2} - 1) = 3 (2 x^{2}) + 3 \cdot - 1 + 2$

Multiply $2$ by $3$ .

$f (2 x^{2} - 1) = 6 x^{2} + 3 \cdot - 1 + 2$

Multiply $3$ by $- 1$ .

$f (2 x^{2} - 1) = 6 x^{2} - 3 + 2$

Step 4

Add $- 3$ and $2$ .

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