Q. 25.0( 1 Vote )
Mark the correct alternative in each of the following:
f: R → R given by
is
A. injective B. surjective
C. bijective D. none of these
Answer :
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.
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