The function f : R→R defined by

Question:

The function $f: R \rightarrow R$ defined by $f(x)=6^{x}+6^{|x|}$ 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 of 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 codomain of the given function.

Hence, Codomain $\neq$ Range

 

Therefore, the given function is into.

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