Answer: The inverse of the logarithmic function f(x) = log2x can be found by interchanging the roles of x and y in the function and solving for y. The steps are as follows:
Step 1: Replace f(x) with y.
y = log2x
Step 2: Interchange x and y.
x = log2y
Step 3: Solve for y.
We need to isolate y on one side of the equation. To do this, we can rewrite the equation in exponential form. Recall that the logarithmic function with base b is defined as follows:
logb(x) = y if and only if b^y = x.
Using this definition, we can rewrite the equation x = log2y as follows:
2^x = y
This means that the inverse of f(x) = log2x is given by:
f –1(x) = 2^x
Therefore, the correct answer is:
f –1(x) = 2^x.
Explanation: