Find the Inverse f(x)=1/4x

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

Step 1

Write $f (x) = \frac{1}{4} x$ as an equation.

$y = \frac{1}{4} x$

Step 2

Interchange the variables.

$x = \frac{1}{4} y$

Step 3

Solve for $y$ .

Rewrite the equation as $\frac{1}{4} y = x$ .

$\frac{1}{4} y = x$

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} y) = 4 x$

Simplify the left side.

Simplify $4 (\frac{1}{4} y)$ .

Combine $\frac{1}{4}$ and $y$ .

$4 \frac{y}{4} = 4 x$

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{y}{4} = 4 x$

Rewrite the expression.

$y = 4 x$

Step 4

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

$f^{- 1} (x) = 4 x$

Step 5

Verify if $f^{- 1} (x) = 4 x$ is the inverse of $f (x) = \frac{1}{4} x$ .

To verify the inverse, check if $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ .

Evaluate $f^{- 1} (f (x))$ .

Set up the composite result function.

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

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

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

Combine $\frac{1}{4}$ and $x$ .

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate $f (f^{- 1} (x))$ .

Set up the composite result function.

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

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

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

Cancel the common factor of $4$ .

Factor $4$ out of $4 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$f (4 x) = x$

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = 4 x$ is the inverse of $f (x) = \frac{1}{4} x$ .

$f^{- 1} (x) = 4 x$

Find the Inverse f(x)=1/4x

Related Questions

Support LCMGCF.com by disabling your adblocker.