• # question_answer 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 $h(x)=f(x)+\text{ }g(x),$ then $h(x)$ is A) one-one onto B) one-one into C) many-one onto D) many-one into

 Since $f(x)$ and $g(x)$are mirror images of each other about the line$y=a,$$f(x)$and $g(x)$are at equal distances from the line $y=a$, Let for some particular ${{x}_{0}}$ $f\left( {{x}_{0}} \right)=a+k,\operatorname{then}\,g\text{ }\left( {{x}_{0}} \right)=a-k,$then $h\left( {{x}_{0}} \right)=f\left( {{x}_{0}} \right)+g\left( {{x}_{0}} \right)=2a$ $\therefore h\left( x \right)=2a\,\,\forall \,\,x\in R.$So,$h(x)$  must be a constant function, which is many -one into.