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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