Mark the correct alternative in each of the following:
f: R → R given by is
Given function is f: R → R given
f(x) = x + √x2
For this function if we take x = 2,
f(x) = 2 + √4
⇒ f(x) =2
For this function if we take x = -2,
f(x) = -2 + √4
⇒ f(x) = 0
So, in general for every negative x, f(x) will be always 0. There is no x ϵ R for which f(x) ϵ (-∞, 0).
Hence, it is neither injective nor surjective and so it is not bijective either.