MCQ
The function $f : R \rightarrow R$ defined by $f(x) = 6^x + 6^{|x|}$ is:
- AOne $-$ one and onto.
- BMany one and onto.
- COne $-$ one and into.
- ✓Many one and into.
✓
Answer
Correct option: 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 co $-$ domain of the given function.
Hence, Co $-$ dornain $=$ Range
Therefore, the given function is into.
$A$ 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 $-$ dornain $=$ Range
Therefore, the given function is into.
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