MCQ
The function f : R $\rightarrow$ 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)
Let $f \left(x_1\right)= f \left(x_2\right)$ for $x_1, x_2 \in R$
$\Rightarrow e ^{x_1}= e ^{x_2}$
$\Rightarrow x_1=x_2$
⇒ f is one one
Let $y= e ^x$
$\Rightarrow \log y=x$
Note that the negative numbers and zero has no pre-image in the domain of the function.
⇒ function f is into.

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