If `f : A rarr B` be any function and if `I_A : A rarr A, I_B : B rarr B` be the identity functions, show that `fo*I_A=f,I_Bof=f`.

If f : R rarr R be defined by f(x)=|x| , show that fof=f

Prove that the identity function f(x) = x is continous

Let A={1,2,3,4} be a given set and f : A rarr A, g : A rarr A be two given functions such that f={(1,4),(2,1),(3,3),(4,2)} g={(1,3),(2,1),(3,2),(4,4)} Find gof, fog, fof, gog .

Let f : R rarr R, f(x)=x^2 and g : R rarr R,g(x)=sinx be two given functions. Is gof=fog ?

If f : R rarr R be defined by f(x)=2x-3 and g : R rarr R be defined by g(x)= (x+3)/2 , show that fog=gof=I_R

If f : R-{-1} rarr R-{1} be defined by f(x)= (x-1)/(x+1) , verify that fof^-1 is an identity function.

Let f : A rarr B, g : B rarr C be two functions such that gof is one-one and onto. Show that f is one-one and g is onto.

A function f : R rarr R is defined as f(x)=10x+7 for all x in R . Find the function g : R rarr R such that gof=fog=I_R .

Prove that the function f : R rarr R, f(x)=5x^3-8 is bijective.

Show that the function f : N' rarr Z, f(x)=100-x^2 is not bijective.