Find the Inverse asin (x)+15

asin $(x) + 15$

Step 1

Interchange the variables.

$x = (y) + 15$

Step 2

Solve for $y$ .

Rewrite the equation as $y + 15 = x$ .

$y + 15 = x$

Subtract $15$ from both sides of the equation.

$y = x - 15$

Step 3

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

$f^{- 1} (x) = x - 15$

Step 4

Verify if $f^{- 1} (x) = x - 15$ is the inverse of $f (x) = (x) + 15$ .

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 $f^{- 1} ((x) + 15)$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} ((x) + 15) = ((x) + 15) - 15$

Combine the opposite terms in $((x) + 15) - 15$ .

Subtract $15$ from $15$ .

$f^{- 1} ((x) + 15) = x + 0$

Add $x$ and $0$ .

$f^{- 1} ((x) + 15) = x$

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

Set up the composite result function.

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

Evaluate $f (x - 15)$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (x - 15) = (x - 15) + 15$

Combine the opposite terms in $(x - 15) + 15$ .

Add $- 15$ and $15$ .

$f (x - 15) = x + 0$

Add $x$ and $0$ .

$f (x - 15) = x$

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = x - 15$ is the inverse of $f (x) = (x) + 15$ .

$f^{- 1} (x) = x - 15$