Question

The function f : R → R defined by $f\left(x\right)=2^x+2^{\left|x\right|}\mathrm{is}$
(a) one-one and onto
(b) many-one and onto
(c) one-one and into
(d) many-one and into

Answer 1

(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$\ne$Range
Therefore, the given function is into.