Question

If f(x)=1/9x-2, what is f^–1(x)?

A.) f^–1(x) = 9x + 18
B.) f^-1(x)=1/9x+2
C.) f^–1(x) = 9x + 2
D.) f^-1(x)=-2x+1/9

Answer 1

f(x)=19x+2→ Switch the f(x) with a y

y=19x+2→ Switch the places of the x and the y variables

x=19y+2→ Solve for y

x−2=19y

y=9x−18

The inverse is f−1(x)=9x−18

Answer 2

Option A is correct

`f^(-1)(x) = 9x+18`

Explanation:

Given the function:

`f(x) =(1)/(9)x-2`

Let y = f(x)

then;

`y=(1)/(9)x-2`

Replace x and y values we have;

`x=(1)/(9)y-2`

Add 2 to both sides we have

`x+2=(1)/(9)y`

Multiply both sides by 9, to solve for y

`9(x+2) = y`

or

y = 9(x+2)

replace
`y = f^(-1) (x)` then;

`f^(-1)(x) = 9(x+2)`

⇒
`f^(-1)(x) = 9x+18`

therefore, the inverse of f(x) is,
`f^(-1)(x) = 9x+18`