Find f(g(x)) f(x)=4x^2 , g(x)=(2x)/4

$f (x) = 4 x^{2}$ , $g (x) = \frac{2 x}{4}$

Set up the composite result function.

$f (g (x))$

Evaluate $f (\frac{2 x}{4})$ by substituting in the value of $g$ into $f$ .

$f (\frac{2 x}{4}) = 4 {(\frac{2 x}{4})}^{2}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x$ .

$f (\frac{2 x}{4}) = 4 {(\frac{2 (x)}{4})}^{2}$

Cancel the common factors.

Factor $2$ out of $4$ .

$f (\frac{2 x}{4}) = 4 {(\frac{2 x}{2 \cdot 2})}^{2}$

Cancel the common factor.

$f (\frac{2 x}{4}) = 4 {(\frac{2 x}{2 \cdot 2})}^{2}$

Rewrite the expression.

$f (\frac{2 x}{4}) = 4 {(\frac{x}{2})}^{2}$

Simplify the expression.

Apply the product rule to $\frac{x}{2}$ .

$f (\frac{2 x}{4}) = 4 (\frac{x^{2}}{2^{2}})$

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

$f (\frac{2 x}{4}) = 4 (\frac{x^{2}}{4})$

Cancel the common factor of $4$ .

Cancel the common factor.

$f (\frac{2 x}{4}) = 4 (\frac{x^{2}}{4})$

Rewrite the expression.

$f (\frac{2 x}{4}) = x^{2}$