Find f(g(x)) f(x)=3x-1 , g(x)=5x^2-2

$f (x) = 3 x - 1$ , $g (x) = 5 x^{2} - 2$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (5 x^{2} - 2)$ by substituting in the value of $g$ into $f$ .

$f (5 x^{2} - 2) = 3 (5 x^{2} - 2) - 1$

Step 3

Simplify each term.

Apply the distributive property.

$f (5 x^{2} - 2) = 3 (5 x^{2}) + 3 \cdot - 2 - 1$

Multiply $5$ by $3$ .

$f (5 x^{2} - 2) = 15 x^{2} + 3 \cdot - 2 - 1$

Multiply $3$ by $- 2$ .

$f (5 x^{2} - 2) = 15 x^{2} - 6 - 1$

Step 4

Subtract $1$ from $- 6$ .

$f (5 x^{2} - 2) = 15 x^{2} - 7$