If `f and g` are one-one functions, then (a)`f+g` is one one (b)`fg` is one one (c)`fog` is one one (d)`n on e of these`

Options

A. `f+g` is one-one
B. `fg` is one-one
C. `fog` is one-one
D. None of these

Answer

C

Explanation

(a) `f(x)=sinx and g(x)=cosx, x in [0, pi//2]`
Here, both f(x) and g(x) are one-one functions.
But `h(x)=f(x)+g(x)=sinx+cosx` is many-one
as ` h(0)=h(pi//2)=1.`
(b) `h(x)=f(x) g(x)=sinx cosx=(sin 2x)/(2)` is many-one,
as `h(0)=h(pi//2)=0.`
(c) It is a fundamental property.