If `f(x)=sinx+cosx `and `g(x)=x^2-1`, then `g(f (x)) `is invertible in the domain .

If f(x)=sinx" and "g(x)=sgn sinx , then g'(1) equals

If f(x)=|x-1|" and "g(x)=f(f(f(x))) , then for xgt2,g'(x) is equal to

Let f(x)=2x-sinx and g(x) = 3^(sqrtx) . Then

Let g(x)=f(sin x)+ f(cosx), then g(x) is decreasing on:

If f(x) = {sinx , x lt 0 and cosx-|x-1| , x leq 0 then g(x) = f(|x|) is non-differentiable for

If f(x)=sin^2x and the composite function g(f(x))=|sinx| , then g(x) is equal to (a) sqrt(x-1) (b) sqrt(x) (c) sqrt(x+1) (d) -sqrt(x)

If f(x)=x-7 and g(x)=sqrt(x) , what is the domain of g@f ?

If f(x)=sinx, g(x)=cosx and h(x)=cos(cosx), then the integral I=int f(g(x)).f(x).h(x)dx simplifies to -lambda sin^(2)(cosx)+C (where, C is the constant of integration). The value of lambda is equal to

If f(x)= sin^(-1)x and g(x)=[sin(cosx)]+[cos(sinx)], then range of f(g(x)) is (where [*] denotes greatest integer function)