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
[tex]y=2^{(x)} + 6[/tex] ------> [tex]x = 2^{(y)}+ 6[/tex]
[tex]x-6 = 2^y[/tex]
[tex]y = log_2(x-6)[/tex]
2) Check. The range of f(x) is the domain of [tex]f^{-1}(x)[/tex].
So if f(a) = b, this means that [tex]f^{-1}(b)[/tex] = a.
[tex]f(2) = 2^2+ 6 = 10[/tex]
[tex]f^{-1}(x) = log_2(10-6) = 2[/tex]
Is fulfilled. Therefore [tex]y=log_2(x-6)[/tex] is the inverse of [tex]f(x) = 2^{(x)} +6[/tex]
