Find f(g(x)) f(x)=4x^2-3 ; g(x)=4/x

$f (x) = 4 x^{2} - 3$ ; $g (x) = \frac{4}{x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (\frac{4}{x}) = 4 {(\frac{4}{x})}^{2} - 3$

Step 3

Simplify each term.

Apply the product rule to $\frac{4}{x}$ .

$f (\frac{4}{x}) = 4 (\frac{4^{2}}{x^{2}}) - 3$

Raise $4$ to the power of $2$ .

$f (\frac{4}{x}) = 4 (\frac{16}{x^{2}}) - 3$

Multiply $4 \frac{16}{x^{2}}$ .

Combine $4$ and $\frac{16}{x^{2}}$ .

$f (\frac{4}{x}) = \frac{4 \cdot 16}{x^{2}} - 3$

Multiply $4$ by $16$ .

$f (\frac{4}{x}) = \frac{64}{x^{2}} - 3$