Find the Inverse y=3(x-4)

$y = 3 (x - 4)$

Step 1

Interchange the variables.

$x = 3 (y - 4)$

Step 2

Solve for $y$ .

Rewrite the equation as $3 (y - 4) = x$ .

$3 (y - 4) = x$

Divide each term in $3 (y - 4) = x$ by $3$ and simplify.

Divide each term in $3 (y - 4) = x$ by $3$ .

$\frac{3 (y - 4)}{3} = \frac{x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (y - 4)}{3} = \frac{x}{3}$

Divide $y - 4$ by $1$ .

$y - 4 = \frac{x}{3}$

Add $4$ to both sides of the equation.

$y = \frac{x}{3} + 4$

Step 3

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

$f^{- 1} (x) = \frac{x}{3} + 4$

Step 4

Verify if $f^{- 1} (x) = \frac{x}{3} + 4$ is the inverse of $f (x) = 3 (x - 4)$ .

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 $f^{- 1} (3 (x - 4))$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} (3 (x - 4)) = \frac{3 (x - 4)}{3} + 4$

Cancel the common factor of $3$ .

Cancel the common factor.

$f^{- 1} (3 (x - 4)) = \frac{3 (x - 4)}{3} + 4$

Divide $x - 4$ by $1$ .

$f^{- 1} (3 (x - 4)) = x - 4 + 4$

Combine the opposite terms in $x - 4 + 4$ .

Add $- 4$ and $4$ .

$f^{- 1} (3 (x - 4)) = x + 0$

Add $x$ and $0$ .

$f^{- 1} (3 (x - 4)) = x$

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

Set up the composite result function.

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

Evaluate $f (\frac{x}{3} + 4)$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (\frac{x}{3} + 4) = 3 ((\frac{x}{3} + 4) - 4)$

Combine the opposite terms in $(\frac{x}{3} + 4) - 4$ .

Subtract $4$ from $4$ .

$f (\frac{x}{3} + 4) = 3 (\frac{x}{3} + 0)$

Add $\frac{x}{3}$ and $0$ .

$f (\frac{x}{3} + 4) = 3 (\frac{x}{3})$

Cancel the common factor of $3$ .

Cancel the common factor.

$f (\frac{x}{3} + 4) = 3 (\frac{x}{3})$

Rewrite the expression.

$f (\frac{x}{3} + 4) = x$

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = \frac{x}{3} + 4$ is the inverse of $f (x) = 3 (x - 4)$ .

$f^{- 1} (x) = \frac{x}{3} + 4$

Find the Inverse y=3(x-4)

Related Questions

Support LCMGCF.com by disabling your adblocker.