Let `f(x)=a x+ba n dg(x)=c x+d , a!=0.` Assume `a=1,b=2.` If `(fog)(x)=(gof)(x)` for all `x ,` what can you say about `ca n dd ?`

Let f(x)=x^2+x+1 and g(x)=sinx . Show that fog!=gof .

If f(x)=e^x and g(x)=(log)_e x(x >0), find fog and gof . Is fog=gof?

Let f(x)=[x] and g(x)=|x| . Find (gof)(5/3) fog(5/3)

Let f(x)=[x] and g(x)=|x| . Find (gof)(5/3) fog(5/3)

If f(x) = 1//x, g(x) = sqrt(x) for all x in (0,oo) , then find (gof)(x).

Let f(x)=x^2 \ a n d \ g(x)=sinx for all x in R . Then the set of all x satisfying (fogogof)(x)=(gogof)(x),w h e r e (fog)(x)=f(g(x)), is

Let f(x)=x^2a n dg(x)=sinxfora l lx in Rdot Then the set of all x satisfying (fogogof)(x)=(gogof)(x),w h e r e(fog)(x)=f(g(x)), is (a) +-sqrt(npi),n in {0,1,2, dot} (b) +-sqrt(npi),n in {1,2, dot} (c) pi/2+2npi,n in { ,-2,-1,0,1,2} (d) 2npi,n in { ,-2,-1,0,1,2, }

Let f(x)=x^2 and g(x)=2^x . Then the solution set of the equation fog(x)=gof(x) is (a)R (b) {0} (c) {0, 2} (d) none of these

Let : R->R ; f(x)=sinx and g: R->R ; g(x)=x^2 find fog and gof .

If f:R -> R, g:R -> R defined as f(x) = sin x and g(x) = x^2 , then find the value of (gof)(x) and (fog)(x) and also prove that gof != fog .