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

Find f0g and g0f : f(x) = 2x , g(x)=sinx

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 .

If f : R rarr R is defined by f(x)=x^2+2 and g : R-{1} rarr R is defined by g(x)=x/(x-1) , find (fog)(x) and (gof)(x) .

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

Let f:R rarr R is defined by f(x)=3x-2 and g:R rarr R is defined by g(x)=(x+2)/3 . Show that f.g=g.f .

Let f : R rarr R be defined as f(x)=x^3+2 . Show that f^-1 : R rarr R exists and hence find the formula for f^-1 .

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.

Find f0g and g0f : f(x) = alpha , g(x)=sinx^2

Let f : R rarr R and g : R rarr R be defined by f(x)=x^2+3x+1 and g(x)=4x-3 . Find formulas defining the compositions fog,gof,fof and gog.

If f(x)=x^2 and g(x)=sin3x then find f0g and g0f Is f0g = g0f ?