Find f(g(x)) f(x)=4x^2-7 , g(x)=2/x

$f (x) = 4 x^{2} - 7$ , $g (x) = \frac{2}{x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (\frac{2}{x}) = 4 {(\frac{2}{x})}^{2} - 7$

Step 3

Simplify each term.

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

$f (\frac{2}{x}) = 4 (\frac{2^{2}}{x^{2}}) - 7$

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

$f (\frac{2}{x}) = 4 (\frac{4}{x^{2}}) - 7$

Multiply $4 \frac{4}{x^{2}}$ .

Combine $4$ and $\frac{4}{x^{2}}$ .

$f (\frac{2}{x}) = \frac{4 \cdot 4}{x^{2}} - 7$

Multiply $4$ by $4$ .

$f (\frac{2}{x}) = \frac{16}{x^{2}} - 7$