Questions
Let be a function defined by . Then
a
f is both one-one and onto
b
f is one-one but not onto
c
f is onto but not one-one
d
f is neither one-one nor onto
detailed solution
Correct option is D
f is not one-one as f (0) = 0 and f (-1) = 0. f is also not onto as for y = 1 there is no x ∈ R such that f (x) = 1. If there is such a x ∈ R then e|x| – e–x = e x + e–x , clearly x≠ 0. For x > 0, this equation gives -e-x=e-x which is not possible. For x < 0, the above equation gives e x = - e–x which is also not possible .Talk to our academic expert!
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