For the function f(x)=5(x−9)

Question

, 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.