To solve the problem, we first recall that two functions whose graphs are symmetric about the line (y=x) are inverse functions of each other.

Step 1: Identify the inverse function

Given (g(x)=2^x), its inverse function (f(x)) is the logarithm function with base 2, i.e., (f(x)=\log_2 x).

This is because:

• For (g(x)=2^x), swapping (x) and (y) gives (x=2^y), solving for (y) gives (y=\log_2 x).

Step 2: Calculate (f(2))

Substitute (x=2) into (f(x)=\log_2 x):
(f(2)=\log_2 2=1).

Answer: (\boxed{1})

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