Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
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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