For the function f(x)=x^2-12, find (f o f^-1)(4)
To find (f o f^-1)(4), we need to first find the inverse function of f(x).
Given the function f(x) = x^2 - 12, let's find its inverse by following these steps:
1. Replace f(x) with y: y = x^2 - 12.
2. Interchange x and y: x = y^2 - 12.
3. Solve for y: x + 12 = y^2.
4. Take the square root of both sides: √(x + 12) = y.
Now, we have the inverse function of f(x): f^-1(x) = √(x + 12).
Next, we can evaluate (f o f^-1)(4) by substituting f^-1(x) into f(x) and then plugging in the value 4:
(f o f^-1)(4) = f(f^-1(4)) = f(√(4 + 12)).
Simplifying inside the function, we get:
(f o f^-1)(4) = f(√16) = f(4).
Now, plug in this value into the original function f(x):
f(4) = 4^2 - 12 = 16 - 12 = 4.
Therefore, (f o f^-1)(4) equals 4.