Question

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

Answer 1

Answer:

$f^{-1}(x) = log_2(x-6)$

Step-by-step 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:

$f^{-1}(x) = log_2(x-6)$