Question:
The function $f: R \rightarrow R$ defined by $f(x)=2^{x}+2^{|x|}$ is
(a) one-one and onto
(b) many-one and onto
(c) one-one and into
(d) many-one and into
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.
From the given graph we can see that the range is $[2, \infty)$
and R is the co-domain of the given function.
Hence, Co-domain
Therefore, the given function is into.
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