Question

If F -1(x) is the inverse of F(x), which statements must be true?
check all that apply
a) f(f-1(x))=x
b) f-1(f(x)=x
c) the range of f-1 is the range of f(x)
d) the range of f-1(x) is the domain of f(x)
e) the domain of f-1(x) is the range of f(x)
f) the domain of f-1(x) is the domain of f(x)

Check all that apply.

A. F(F -1(x)) = x
B. F -1(F(x)) = x
C. The range of F -1(x) is the range of F(x).
D. The range of F -1(x) is the domain of F(x).
E. The domain of F -1(x) is the range of F(x).
F. The domain of F -1(x) is the domain of F(x).

Answer 1

Hint: If (a,b) is a point on the graph of f, then (b,a) is a point on the graph of the inverse of f.

Answer 2

\[f(a)=b \implies f^{-1}(b)=a \\ \text{ so what does } f(f^{-1}(b))=? \\ \text{ or what does } f^{-1}(f(a))="?\]

Answer 3

I will point on one more thing about the hint...
notice that a is in the domain of f but a is in the what of inverse of f?

Answer 4

and notice that b is in the range of f but b is in the what of inverse of f?