Answer:
f^(-1)(x) = (x - 1/4) / 3
Explanation:
Start with the original function:
f(x) = 3x + 1/4
Swap f(x) and x:
x = 3f^(-1)(x) + 1/4
Now, solve for f^(-1)(x), which is the inverse function:
First, subtract 1/4 from both sides:
x - 1/4 = 3f^(-1)(x)
Divide both sides by 3 to isolate f^(-1)(x):
(x - 1/4) / 3 = f^(-1)(x)
So, the inverse function f^(-1)(x) is:
f^(-1)(x) = (x - 1/4) / 3