If $f\left(x\right)=2x$ and $g$ is identity function, then:

Q. f(x) =sin^2x, g(x) is polynomial function and f(g(x))is periodic. If g(1)= 5 and g(5) 1, then g(0) is

Q. let f and g be differentiable functions on R such that fog is the identity functions. If for some, a, b ϵ R, g'(a) = 5 and g(a) = b, then, f'(b) is equal to (1) 1/5 (2) 1 (3) 2/5 (4) 5

Q. If $f$ and $g$ be differentiable function satisfying $g^{\prime }\left(a\right)=2,g\left(a\right)=b$ and $fog=I$ (identity function), then $f^{\prime }\left(b\right)$ is equal to

Q. $f:(0,\infty )\to R$ is continuous. If $F\left(x\right)$ is a differentiable function such that $F\left(x\right)=f\left(x\right),\forall x>0$ and $f\left(x^2\right)=x^2+x^3$, then $f\left(4\right)$ equals

Q. Let $f$ and $g$ be differentiable functions satistying $g^{\prime }\left(a\right)=2,g\left(a\right)=b$ and $fog=I$ ( identity function) Then $f^{\prime }\left(b\right)$ is equal to-