Question

Find f-l.
f(x) = 4log (x-7)

Answer 1

The answer is +7. I agree with the person above

Answer 2

f⁻¹(x) =
`2^{(x)/(4) }` + 7

Explanation:

The inverse of a function reverses the operations performed by the function in the question such if f(x) = y, then we have, f⁻¹(y) = x, which reverses the operation of the first function.

The inverse of a function f(x) = 4·㏒₂(x - 7) is found as follows;

We have;

y = 4·㏒₂(x - 7)

We substitute x for y to get;

x = 4·㏒₂(y - 7) which gives;

x/4 = ㏒₂(y - 7)

`2^{(x)/(4) }` = y - 7

y =
`2^{(x)/(4) }` + 7

Therefore;

f⁻¹(x) =
`2^{(x)/(4) }` + 7.