The function $f : R \to R$ 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

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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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