Given f(x)=7x-7
(f∘f^-1)(-7)=
To find (f∘f^-1)(-7), we need to evaluate the composite function f(f^-1(x)) at x = -7.
First, let's find the inverse function f^-1(x):
f(x) = 7x - 7
y = 7x - 7 (replace f(x) with y)
x = 7y - 7 (switch x and y)
7y = x + 7 (add 7 to both sides)
y = (x + 7)/7 (divide by 7)
So, f^-1(x) = (x + 7)/7.
Now, let's evaluate f(f^-1(x)) at x = -7:
f(f^-1(-7)) = f(((-7) + 7)/7) = f(0/7) = f(0) = 7(0) - 7 = -7
Therefore, (f∘f^-1)(-7) = -7.