Given f(x)=8x-8 find the value below.
(f∘f^-1)(-8)
To find the value of (f∘f^-1)(-8), we need to find the composition of f with its inverse, and then evaluate it at -8.
First, let's find the inverse of f(x):
f(x) = 8x - 8
To find the inverse, we can switch x and y and solve for y:
x = 8y - 8.
Solving for y:
8y = x + 8
y = (x + 8)/8
So the inverse function is f^-1(x) = (x + 8)/8.
Now, let's find (f∘f^-1)(-8):
(f∘f^-1)(-8) = f(f^-1(-8))
First, let's evaluate f^-1(-8):
f^-1(-8) = (-8 + 8)/8 = 0/8 = 0
Now, substitute f^-1(-8) = 0 into f(x):
f(0) = 8(0) - 8 = 0 - 8 = -8
Therefore, (f∘f^-1)(-8) = -8.