Find f(g(x)) f(x)=4x , g(x)=-1/(4x)

$f (x) = 4 x$ , $g (x) = - \frac{1}{4 x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (- \frac{1}{4 x})$ by substituting in the value of $g$ into $f$ .

$f (- \frac{1}{4 x}) = 4 (- \frac{1}{4 x})$

Step 3

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4 x}$ into the numerator.

$f (- \frac{1}{4 x}) = 4 (\frac{- 1}{4 x})$

Factor $4$ out of $4 x$ .

$f (- \frac{1}{4 x}) = 4 (\frac{- 1}{4 (x)})$

Cancel the common factor.

$f (- \frac{1}{4 x}) = 4 (\frac{- 1}{4 x})$

Rewrite the expression.

$f (- \frac{1}{4 x}) = \frac{- 1}{x}$

Step 4

Move the negative in front of the fraction.

$f (- \frac{1}{4 x}) = - \frac{1}{x}$