The function f:R R defined by f(x) = e^x is - Vidyadip

MCQ

The function $f:R \to R$ defined by $f(x) = {e^x}$ is

A
Onto
B
Many-one
✓
One-one and into
D
Many one and onto

✓

Answer

Correct option: C.

One-one and into

c
(c) Function $f:R \to R$ is defined by $f(x) = {e^x}$.

Let ${x_1},\,{x_2} \in R$ and $f({x_1}) = f({x_2})$ or ${e^{{x_1}}} = {e^{{x_2}}}$ or ${x_1} = {x_2}$.

Therefore $f$ is one-one. Let $f(x) = {e^x} = y$.

Taking $log$ on both sides, we get $x = \log y$.

We know that negative real numbers have no pre-image or the function is not onto and zero is not the image of any real number.

Therefore function $f$ is into.

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