Question

What is the inverse of the following function? y= 2^x + 3

Answer 1

Answer:

Option B: $y=log_2(x-3)$

Step-by-step explanation:

To obtain the inverse of the function $y= 2^x + 3$, you need to solve the equation for the variable "x":

$y= 2^x + 3\\\\y-3=2^x\\\\log_2(y-3)=log_2(2^x)\\\\x=log_2(y-3)$

Now you need to exchange the variable "x" with the variable "y". Then:

$y=log_2(x-3)$

Finally, you get that the inverse of the function $y= 2^x + 3$ is:

$y=log_2(x-3)$

This matches with the option B.