If $f(x)=-|x|$, then $(f \circ f \circ f)(x) + (f \circ f \circ f)(-x) =$

If $f$ is the greatest integer function and $g$ is the modulus function,then $(gof)\left( -\frac{5}{3} \right) - (fog)\left( -\frac{5}{3} \right) = $

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$, where $[x]$ is the greatest integer not exceeding $x$, then for every $x \in R, f(g(x))$ is equal to

Let $f(x) = e^x$ and $g(x) = x^2$. Then,the number of solutions of $f(g(x)) = g(f(x))$ is equal to:

Let $f(x) = \sin x$ and $g(x) = \cos x$. Which of the following statements is false?

If $f(x)=e^x$ and $h(x)=(f \circ f)(x)$, then $\frac{h^{\prime}(x)}{h(x)}=$