List of top Mathematics Questions on composite of functions asked in KCET

Let f(x) = sin 2x + cos 2x and g(x)=x²-1, then g(f(x)) is invertible in the domain

If f(x) and g(x) are two functions with g(x) = \(x-\frac{1}{x}\) and fog(x) = \(x^3-\frac{1}{x^3}\) then f'(x) =

If the function of f(x) = \(\frac{1}{x+2}\), then the point of discontinuity of the composite function y = f(f(x)) is

Let f : R→R be defined by f(x)= 3x²-5 and g : R→R by g(x)=\(\frac{x}{x^2+1}\) then gof is

If \(f(1) = 1, \quad f'(1) = 3\) then the derivative of \(f(f(f(x))) + (f(x))^2\) at \(x= 1\) is