Question

What is the inverse of the function below?

f(x) = 2^x + 6

Answer 1

The inverse of this function would be f(x) =
`(Log(x - 6))/(Log2)`.

You can find the value of any inverse function by switching the f(x) and the x value. Then you can solve for the new f(x) value. The end result will be your new inverse function. The step-by-step process is below.

f(x) =
`2^(x)` - 6 ----> Switch f(x) and x

x =
`2^(f(x))` - 6 ----> Add 6 to both sides

x + 6 =
`2^(f(x))` -----> Take the logarithm of both sides in order to get the f(x) out of the exponent

Log(x + 6) = f(x)Log2 ----> Now divide both sides by Log2

`(Log(x + 6))/(Log2)` = f(x) ----> And switch the order for formatting purposes.

f(x) =
`(Log(x + 6))/(Log2)`

And that would be your new inverse function.

Answer 2

f^-1 (x) = log 2 (x-6)

Explanation: