Question

What is the inverse of the function of (x)=2^(x)+6

Answer 1

Answer:

Option D.

Step-by-step explanation:

To find the inversion of a function follow the following procedure

1) Replace x with y in the function and clear y

$y=2^{(x)} + 6$ ------>  $x = 2^{(y)}+ 6$

$x-6 = 2^y$

$y = log_2(x-6)$

2) Check. The range of f(x) is the domain of $f^{-1}(x)$.

So if f(a) = b, this means that $f^{-1}(b)$ = a.

$f(2) = 2^2+ 6 = 10$

$f^{-1}(x) = log_2(10-6) = 2$

Is fulfilled. Therefore $y=log_2(x-6)$ is the inverse of $f(x) = 2^{(x)} +6$