Question

If f(x) = 4x + 7, which of the following is the inverse of f(x)?

O A. f-'(x) = 4x - 7
O B. f'() = *=4
C. FGx) = 7 - 4x
O D. F"(x) = *z?

Answer 1

For this case we must find the inverse of the following function:

`f (x) = 4x + 7`

For it:

Replace f (x) with y:

`y = 4x + 7`

We exchange the variables:

`x = 4y + 7`

We solve for y:

We subtract 7 on both sides of the equation:

`x-7 = 4y`

We divide between 4 on both sides of the equation:

`y = \frac {x} {4} - \frac {7} {4}`

Finally, we change y by
`f ^ {- 1} (x)`:

`f ^ {- 1} (x) = \frac {x} {4} - \frac {7} {4}`

ANswer:

`f ^ {- 1} (x) = \frac {x} {4} - \frac {7} {4}`