Let $f:R\to R$ and $g:R\to R$ be two one-one and onto functions such that they are mirror images of each other about the line $y=a$. If $h\left(x\right)=f\left(x\right)+g\left(x\right),$ then $h\left(x\right)$ is

Let $f\left(x\right)=x^2$ and $g\left(x\right)=\sin x$ for all $x\in R.$ Then the set of all $x$ satisfying $(f\circ g\circ g\circ f)\left(x\right)=(g\circ g\circ f)\left(x\right),$ where $(f\circ g)\left(x\right)=f\left(g\right(x\left)\right),$ is

The function $f: \left[0,3\right]\to \left[1,29\right],$ defined by $f\left(x\right)=2x^3-15x^2+36x+1,$ is