Question

How do you find the inverse of `f(x)=log(x+15)`?

Answer 1

Set `y=f(x)` and solve with respect to `x` hence you get

`y=log(x+15)=>x+15=10^y=>x=10^y-15`

Now it is `f^-1(x)=10^x-15`

Assuming that `log10=1`

Answer 2

`f^-1(x) = 10^x -15`

Explanation:

For any inverse function of `f(x), f^-1(x)`
`f(f^-1(x)) = x`
`f(f^-1(x+15)) = log(f^-1(x+15)) = log(f^-1(x) + 15)`
`10^x = f^-1(x) +15`
`f^-1(x) = 10^x -15`

Alternatively:
`u = x + 15; x = u -15`
`y = log_b u; b^y = u; b = 10; 10^y = u` substitute for u
`10^y = x+15; x = 10^y -15` replace y by x and write
`f^-1(x) = 10^x -15` which is exactly as above