Consider of `f : N rarrN` and `h : N rarr R` defined as f(x) = 2x, g(y) = 3y + 4
and h(z) = sin z,`AA`, x, y and z in N. Show that ho(gof) = (hog)of.

Let f, g: R rarr R be defined by f(x)=x^2+1 and g(x)=sin x . Find f o g and gof .

If f: RrarrR be defined by f(x)=2x-3 and g:RrarrR be defined by g(x)=(x+3)/2 .Show that fog=I_R=gof

Prove that the function f: N rarr N , defined by f(x)=x^2+x+1 is one-one but not onto.

Let N rarr R be a function defined as f(x) = 4x^2 + 12x +15 Show that f : N rarr S , where, S is the range of f, is invertible. Find the inverse of f.

If x,y,z are in G.P. and a^(x)=b^(y) =c^(z) then

Let R be the relation on the set Z of all integers defined by R={(x, y) : x,y in Z,x-y is divisible by n}.Prove that i) (x, x) in R for all x in , Z ii) (x, y) in R implies that (y, x) in R for all x, y in Z iii) (x, y) in R and (y, z) in R implies that (x, z) in R for all x, y, z in Z