Question

Find the inverse of the given function f(x) =2^x+6

Answer 1

`f^(-1)(x) = log_2(x-6)`

Explanation:

To find the inverse
`f^(-1)(x)` of a function follow the following steps.

1) Do y = f (x)

`f(x) =y= 2 ^ x + 6`

`y= 2 ^ x + 6`

2) Solve the equation for the variable x.

`y= 2 ^ x + 6\\\\y-6 = 2^x\\\\log_2(y-6) = x\\\\x=log_2(y-6)`

3) exchange the variable y with the variable x

`x=log_2(y-6)\\\\y=log_2(x-6)`

Finally the inverse is:

`f^(-1)(x) = log_2(x-6)`