To find the value of f(13), we first need to evaluate the function f(x) defined as:
f(x) = 3x + 1
Now, let’s compute f(13):
f(13) = 3(13) + 1
Calculating this gives us:
f(13) = 39 + 1 = 40
Therefore, the value of f(13) is:
40
Next, since it’s stated that f(1) is the inverse of f, let’s find f(1) to understand its implications:
f(1) = 3(1) + 1 = 4
For the inverse function, we denote it as f-1. The relationship of a function and its inverse is given by:
f(f-1(x)) = x and f-1(f(x)) = x
To find the inverse function f-1(y), we start from:
y = 3x + 1
Now, solving for x:
- Rearranging the equation gives us: y – 1 = 3x
- Then, we have: x = (y – 1)/3
This means the inverse function is:
f-1(y) = (y – 1)/3
From this, we can see that f(1) = 4 clearly satisfies the relationship with the inverse. We can verify this:
f(f-1(4)) = 4
Calculating:
f( (4 – 1)/3 ) = f(1) = 4
Thus, everything is consistent. In summary, the value of f(13) is:
40