Answer to Question #25072 in Discrete Mathematics for sakura

Question

Prove:
1. Show that f: R implies R given by f(x)=x^3 is bijective while g:R implies R given by g(x)=((x)^2)-1
2. Let A, B non empty sets f: A implies B. Show that f-1(f inverse) o f is an equivalent relation on A.
3. If f: A implies b is one to one and onto then f-1(f inverse) is also one to one correspondence.
4. Let f: A implies B and g: B implies C be one to one correspondence. Then g o f : A implies C is one to one correspondence.
5. Let f: A implies B and g: B implies C be one to one correspondence. Then (g o f)^-1 (x)=(f^-1 o g^-1) (x) = f^-1(g^-1 (x))