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Question
The function \[f : R \to R\] defined by
\[f\left( x \right) = 6^x + 6^{|x|}\] 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 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
\[[2, \infty )\]b
and R is the codomain of the given function .
Hence, Codomain
\[\neq\] Range
Therefore, the given function is into .
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