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

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

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 $f$ .

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

Step 3

Combine $2$ and $\frac{1}{2 x}$ .

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

Step 4

Reduce the expression $\frac{2}{2 x}$ by cancelling the common factors.

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Multiply the numerator by the reciprocal of the denominator.

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

Step 6

Multiply $x$ by $1$ .

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