Question

If f(x)= 3x+6 which of the following is the inverse of f(x)

Answer 1

f(x)^-1 = 1/3x - 2

Explanation:

Replace f(x) with y and solve:

y = 3x + 6

Swap x and y

x = 3y + 6

Now isolate y

x/3 = 3y/3 + 6/3

1/3 x = y + 2

1/3 x - 2 = y + 2 - 2

y = 1/3x - 2 or f(x)^-1 = 1/3x - 2

Answer 2

For this case we have the following function:

`f (x) = 3x + 6`

We must find the inverse of the function, then:

Replace f (x) with y:
`y = 3x + 6`

We exchange the variables:

`x = 3y + 6`

We solve for "y":

Subtracting 6 on both sides of the equation:

`x-6 = 3y`

Dividing between 3 on both sides of the equation:

`y = \frac {x} {3} - \frac {6} {3}\\y = \frac {x} {3} -2`

We change y by
`f ^ {- 1} (x)`, and finally we have:

`f ^ {- 1} (x) = \frac {x} {3} -2`

ANswer:

`f ^ {- 1} (x) = \frac {x} {3} -2`