Relations and Functions — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions1 Mark
Question
Let $\;f{\text{ }}:{\text{ }}R{\text{ }} \to {\text{ }}R$ be defined as f (x) = 3x. Choose the correct answer.
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Answer
Injectivity: Let ${x_1},{x_2} \in R\;$ such that $f\left( {{x_1}} \right) = f\left( {{x_2}} \right).$ Then, $f\left( {{x_1}} \right) = f\left( {{x_2}} \right)$$ \Rightarrow $3${x_1} = 3{x_2}$$ \Rightarrow $${x_1} = {x_2}\;.$ So, f : R $\rightarrow$ R is one –one. Surjectivity: Let y$\; \in $ R, Then $f(x) = y \Rightarrow 3x = y \Rightarrow x = \frac{y}{3}$, Clearly, $\frac{y}{3} \in R\;for\;any\;y \in R$ such that $f\;\left( {\frac{y}{3}} \right) = 3\left( {\frac{y}{3}} \right) = y\;.$ So, Let f : ${\text{ }}R{\text{ }} \to {\text{ }}R$ is onto.
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