Question

For the function f(x)=5(x−9)
, find f−1(x)
.(1 point)
Responses

f−1(x)=x5+9
f inverse of x is equal to x over 5 plus 9

f−1(x)=x5−9
f inverse of x is equal to x over 5 minus 9

f−1(x)=5(x+9)
f inverse of x is equal to 5 times open paren x plus 9 close paren

f−1(x)=5x+9
f inverse of x is equal to 5 x plus 9

Answer 1

To find the inverse of the function \( f(x) = 5(x - 9) \), we can follow these steps:

1. **Replace \( f(x) \) with \( y \)**:
\[
y = 5(x - 9)
\]

2. **Swap \( x \) and \( y \)**:
\[
x = 5(y - 9)
\]

3. **Solve for \( y \)**:
- First, divide both sides by 5:
\[
\frac{x}{5} = y - 9
\]
- Then, add 9 to both sides:
\[
y = \frac{x}{5} + 9
\]

4. **Replace \( y \) with \( f^{-1}(x) \)**:
\[
f^{-1}(x) = \frac{x}{5} + 9
\]

Therefore, the correct response is:
\[
f^{-1}(x) = \frac{x}{5} + 9
\]

In text form, this is the same as saying:
**f inverse of x is equal to x over 5 plus 9.**