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Question
The function f : R → R defined by
`f (x) = 2^x + 2^(|x|)` is
Options
one-one and onto
many-one and onto
one-one and into
many-one and into
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Solution
(d) many-one and into
Graph for the given function is as follows.
A line parallel to X axis is cutting the graph at two different values.
Therefore, for two different values of x we are getting the same value of y.
That means it is many one function.[2 , ∞ ) and R is the co-domain of the given function.
Hence, Co-domain ≠ Range Therefore, the given function is into.
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