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+x+1 and g(x)=sinx . Show that fog!=gof .

Let f(x)=x amd g(x)=|x| for all x in R . Then the function phi(x)"satisfying"{phi(x)-f(x)}^(2)+{phi(x)-g(x)}^(2) =0 is

Let f(x) = e^(x)- x and g(x) = x^(2) - x , AA x in R . Then, the set of all x in R , when the function h(x)= (fog)(x) is increasing, in

Let f(x) = x+5 and g(x) = x -5 , x in R . Find (fog)(5).

Let g(x) =f(x)-2{f(x)}^2+9{f(x)}^3 for all x in R Then

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

Consider f (x) = x ^(ln x), and g (x) = e ^(2) x. Let alpha and beta be two values of x satisfying f (x) = g(x)( alpha lt beta) If h (x) = (f (x))/(g (x)) then h'(alpha) equals to:

Let f,g:vec R be defined by f(x)=2x+1 and g(x)=x^2-2 for all x in R, respectively. Then, find gof

If f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1, then in this interval