Find f(g(x)) f(x)=-2x , g(x)=1/(2x)

$f (x) = - 2 x$ , $g (x) = \frac{1}{2 x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{1}{2 x})$ by substituting in the value of $g$ into $f$ .

$f (\frac{1}{2 x}) = - 2 \frac{1}{2 x}$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$f (\frac{1}{2 x}) = 2 (- 1) (\frac{1}{2 x})$

Factor $2$ out of $2 x$ .

$f (\frac{1}{2 x}) = 2 (- 1) (\frac{1}{2 (x)})$

Cancel the common factor.

$f (\frac{1}{2 x}) = 2 \cdot (- 1 \frac{1}{2 x})$

Rewrite the expression.

$f (\frac{1}{2 x}) = - 1 \frac{1}{x}$

Step 4

Rewrite $- 1 \frac{1}{x}$ as $- \frac{1}{x}$ .

$f (\frac{1}{2 x}) = - \frac{1}{x}$