To find the value of f^-1(8), we need to use the fact that f(x) and f^-1(x) are inverse functions of each other.
Let's start by finding the inverse function of f(x) = 2x + 5. To do this, we'll interchange x and y and solve for y.
1. Replace f(x) with y: y = 2x + 5.
2. Interchange x and y: x = 2y + 5.
3. Solve for y: x - 5 = 2y.
Divide both sides by 2: (x - 5) / 2 = y.
Therefore, the inverse function is f^-1(x) = (x - 5) / 2.
Now, to find f^-1(8), substitute x = 8 into the inverse function:
f^-1(8) = (8 - 5) / 2 = 3 / 2 = 1.5
Therefore, f^-1(8) equals 3/2 or 1.5.