Answer:
Option B: [tex]y=log_2(x-3)[/tex]
Step-by-step explanation:
To obtain the inverse of the function [tex]y= 2^x + 3[/tex], you need to solve the equation for the variable "x":
[tex]y= 2^x + 3\\\\y-3=2^x\\\\log_2(y-3)=log_2(2^x)\\\\x=log_2(y-3)[/tex]
Now you need to exchange the variable "x" with the variable "y". Then:
[tex]y=log_2(x-3)[/tex]
Finally, you get that the inverse of the function [tex]y= 2^x + 3[/tex] is:
[tex]y=log_2(x-3)[/tex]
This matches with the option B.
