Answer:
The answer is D
Step-by-step explanation:
In order to find out the inverse of the function, you have to express a new function where the independent variable must be "y" instead of "x".
So, you have to reorganize the base function and then free the variable "x".
[tex]f(x)=2^x+6\\f(x)=y\\y=2^x+6\\2^x=y-6\\log_2(2^x)=log_2(y-6)\\x*log_2(2)=log_2(y-6)\\log_2(2)=1\\x=log_2(y-6)\\[/tex]
Then, we recall "y" as "x" and [tex]x=f^-^1(x)[/tex]
Finally, the answer is:
[tex]f^-^1(x)=log_2(x-6)[/tex]
