Let `f:R->R` and `g:R->R` be two one-one and onto functions such that they are mirror images of each other about the line `y=a`. If `h(x)=f(x)+g(x)`, then `h(x)` is (A) one-one onto (B) one-one into (D) many-one into (C) many-one onto

Explanation

y = f(x) and y = g(x) are mirror image of each other about y = a.
` (##CEN_GRA_C01_S01_012_S01.png" width="80%">
For some `x = b, g(b) - a - f(b)`
` rArr f(b) + g(b) = 2a`
` rArr h(b) = f(b) + g(b) = 2a` (constant)
Hence h (x) is a constant function. Thus, it is neither one-one, nor onto.