MCQ
The function $f : R \rightarrow R$ defined by $f(x) = 2^x + 2^{|x| }$ is$:$
- AOne$-$one and onto.
- BMany$-$one and onto.
- ✓One$-$one and into.
- DMany$-$one and into.
✓
Answer
Correct option: C.
One$-$one and into.
The function $f : R \rightarrow R$ defined by $f(x) = 2^x + 2^{|x|}$
Here, for each value of $x$ we will get different values of $f(x).$
Hence, it is one$-$one function.
Also, each element of codomain is mapped to at most one element of the domain.
Function is one$-$one and into.
Here, for each value of $x$ we will get different values of $f(x).$
Hence, it is one$-$one function.
Also, each element of codomain is mapped to at most one element of the domain.
Function is one$-$one and into.
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