The function f : R R defined by f(x) = 2^x + 2^ |x| is: - Vidyadip

MCQ

The function $f : R \rightarrow R$ defined by $f(x) = 2^x + 2^{|x| }$ is$:$

A
One$-$one and onto.
B
Many$-$one and onto.
✓
One$-$one and into.
D
Many$-$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.

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