Find f(g(x)) f(x)=3x^2+4 , g(x)=5x

$f (x) = 3 x^{2} + 4$ , $g (x) = 5 x$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (5 x)$ by substituting in the value of $g$ into $f$ .

$f (5 x) = 3 {(5 x)}^{2} + 4$

Step 3

Simplify each term.

Apply the product rule to $5 x$ .

$f (5 x) = 3 (5^{2} x^{2}) + 4$

Raise $5$ to the power of $2$ .

$f (5 x) = 3 (25 x^{2}) + 4$

Multiply $25$ by $3$ .

$f (5 x) = 75 x^{2} + 4$