Answer:
f^-1(x) = log2(f^-1(x) – 1 + 3).
Explanation:
The inverse of a function "f" is denoted as "f^-1", and it reverses the effect of the original function. In other words, if "f(x)" is a function that maps some input "x" to an output "y", then the inverse function "f^-1(x)" would map the output "y" back to the original input "x".
In this case, to find the inverse of the function f(x) = 2^x + 1 – 3, we can follow these steps:
Swap the roles of x and y in the original equation to obtain y = 2^x + 1 – 3.
Solve for x in terms of y to obtain x = log2(y – 1 + 3).
Replace y with the inverse function notation f^-1 to obtain f^-1(x) = log2(f^-1(x) – 1 + 3).
Therefore, the inverse of the given function f(x) = 2^x + 1 – 3 is f^-1(x) = log2(f^-1(x) – 1 + 3).