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Relations and Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions1 Mark
MCQ
In which of the function is onto defined in $R \rightarrow R$.
  • A
    $f(x)=|x|$
  • B
    $f(x)=e^{-x}$
  • ✓
    $f(x)=x^3$
  • D
    $f(x)=\sin x$.
✓

Answer

Correct option: C.
$f(x)=x^3$
(C) $
f(x)=x^3
$
Here $f: R \rightarrow R$
and$
f(x)=x^3
$
Suppose $y \in R$ co-domain if possible then pre image of $y$ in domain R is $x$.$
\begin{array}{c}
f(x)=y \\
\Rightarrow y=x^3 \therefore x=(y)^{1 / 3} \in R \forall y \in R
\end{array}
$
So, every value $y$ has exist pre image in domain R .
So, $f$ is onto function.

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