Let $f:R\to R$  and $g:R\to R$  be two one-one and onto functions such that they are the 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

Since $f\left(x\right)$  and $g\left(x\right)$  are mirror images of each other about the line $y=a$ , $f\left(x\right)$  and $g\left(x\right)$ are at equal distances from the line $y=a$ .

Let for some particular $x_0$

$f\left(x_0\right)=a+k$ , then $g\left(x_0\right)=a-k$ , then $h\left(x_0\right)=f\left(x_0\right)+g\left(x_0\right)=2a$

$\therefore h\left(x\right)=2a\forall x\in R$ .