Find the Inverse y=9-x

$y = 9 - x$

Interchange the variables.

$x = 9 - y$

Solve for $y$ .

Tap for more steps…

Rewrite the equation as $9 - y = x$ .

$9 - y = x$

Subtract $9$ from both sides of the equation.

$- y = x - 9$

Multiply each term in $- y = x - 9$ by $- 1$

Tap for more steps…

Multiply each term in $- y = x - 9$ by $- 1$ .

$(- y) \cdot - 1 = x \cdot - 1 + (- 9) \cdot - 1$

Multiply $(- y) \cdot - 1$ .

Tap for more steps…

Multiply $- 1$ by $- 1$ .

$1 y = x \cdot - 1 + (- 9) \cdot - 1$

Multiply $y$ by $1$ .

$y = x \cdot - 1 + (- 9) \cdot - 1$

Simplify each term.

Tap for more steps…

Move $- 1$ to the left of $x$ .

$y = - 1 \cdot x + (- 9) \cdot - 1$

Rewrite $- 1 x$ as $- x$ .

$y = - x + (- 9) \cdot - 1$

Multiply $- 9$ by $- 1$ .

$y = - x + 9$

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

Tap for more steps…

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

$f^{- 1} (x) = - x + 9$

Set up the composite result function.

$g (f (x))$

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

$g (9 - x) = - (9 - x) + 9$

Simplify each term.

Tap for more steps…

Apply the distributive property.

$g (9 - x) = - 1 \cdot 9 + x + 9$

Multiply $- 1$ by $9$ .

$g (9 - x) = - 9 + x + 9$

Multiply $- - x$ .

Tap for more steps…

Multiply $- 1$ by $- 1$ .

$g (9 - x) = - 9 + 1 x + 9$

Multiply $x$ by $1$ .

$g (9 - x) = - 9 + x + 9$

Combine the opposite terms in $- 9 + x + 9$ .

Tap for more steps…

Add $- 9$ and $9$ .

$g (9 - x) = x + 0$

Add $x$ and $0$ .

$g (9 - x) = x$

Since $g (f (x)) = x$ , $f^{- 1} (x) = - x + 9$ is the inverse of $f (x) = 9 - x$ .

$f^{- 1} (x) = - x + 9$

Find the Inverse y=9-x

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our
App from the store