Find the Inverse Function f(x)=1/2x

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

Replace $f (x)$ with $y$ .

$y = \frac{1}{2} x$

Interchange the variables.

$x = \frac{1}{2} y$

Solve for $y$ .

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Rewrite the equation as $\frac{1}{2} y = x$ .

$\frac{1}{2} y = x$

Multiply both sides of the equation by $2$ .

$2 \cdot \frac{1}{2} \cdot y = 2 \cdot x$

Simplify $2 \cdot \frac{1}{2} \cdot y$ .

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Cancel the common factor of $2$ .

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Cancel the common factor.

$2 \cdot \frac{1}{2} \cdot y = 2 \cdot x$

Rewrite the expression.

$1 \cdot y = 2 \cdot x$

Multiply $y$ by $1$ .

$y = 2 \cdot x$

$y = 2 x$

Solve for $y$ and replace with $f^{- 1} (x)$ .

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Replace the $y$ with $f^{- 1} (x)$ to show the final answer.

$f^{- 1} (x) = 2 x$

Set up the composite result function.

$g (f (x))$

Evaluate $g (f (x))$ by substituting in the value of $f$ into $g$ .

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

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Since $g (f (x)) = x$ , $f^{- 1} (x) = 2 x$ is the inverse of $f (x) = \frac{1}{2} x$ .

$f^{- 1} (x) = 2 x$

Find the Inverse Function f(x)=1/2x

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