Question

If f(x) = 6x – 4, then f^-1(x)=

Answer 1

`f^(-1)(x)=(x)/(6)+(2)/(3)`

Explanation:

Given function.

`f(x)=6x-4`

To find the inverse function
`f^(-1)(x)`

Step 1:

Replace
`f(x)` with
`y` in the function.

`y=6x-4`

Step 2:

Interchange
`y` with
`x` in the equation.

`x=6y-4`

Step 3:

Solve for
`y`.

We have
`x=6y-4`

Adding 4 to both sides,

`x+4=6y-4+4`

`x+4=6y`

Dividing each term by 6 to isolate
`y`

`(x)/(6)+(4)/(6)=(6y)/(6)`

`(x)/(6)+(4)/(6)=y`

Simplifying fractions by dividing the numerator and denominator by their GCF.

`(x)/(6)+(4/ 2)/(6/ 2)=y`

`(x)/(6)+(2)/(3)=y`

Thus the equation of
`y` is:

`y=(x)/(6)+(2)/(3)`

Step 4:

Replace
`y` with
`f^(-1)(x)`

`f^(-1)(x)=(x)/(6)+(2)/(3)` (Answer)

Thus, we have the inverse function