Question

Which is the inverse of the function f(x)=4x-9

Answer 1

To find the inverse of a function, switch the x and the y (the f(x) = y), then solve for y.

x = 4y - 9

x + 9 = 4y

y = (x+9)/4

So f^-1(x) = (x+9)/4

Answer 2

`f(x)^(-1)` =
`(x+9)/(4)`.

Explanation:

Given : f(x)=4x-9.

To find : Which is the inverse of the function.

Solution : We have given f(x)=4x-9.

Step 1 : replace y to x

x = 4y -9.

Step 2: solve for y

On adding by 9 both side

x + 9 = 4y

On dividing by 4 both sides

y =
`(x+9)/(4)`.

y =
`f(x)^(-1)`.

Then
`f(x)^(-1)` =
`(x+9)/(4)`.

Therefore,
`f(x)^(-1)` =
`(x+9)/(4)`.