If f(x) = 3x + 1 and f(1) is the inverse of f, what is the value of f(13)?

To find the value of f(13) given f(x) = 3x + 1, we first need to understand the function and its inverse.

We can start by substituting 13 into the function:

f(13) = 3(13) + 1 = 39 + 1 = 40

Now, let’s verify the function and its inverse. We know that if f(1) is the inverse of f, then:

f(1) = 3(1) + 1 = 3 + 1 = 4

To find the inverse function, we start from f(x):

y = 3x + 1

Next, we solve for x in terms of y:

y - 1 = 3x
x = (y - 1) / 3
f-1(y) = (y - 1) / 3

Now, if we put 4 into the inverse function:

f-1(4) = (4 - 1) / 3 = 3 / 3 = 1

This confirms that f(1) = 4 is indeed correct. So now our calculation for f(13) holds true. Therefore:

The value of f(13) is 40.