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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