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  • Provide solution for RD Sharma maths class12 Chapter Functions exercise 2.1 question 5 sub question (xv)

Provide solution for RD Sharma maths class12 Chapter Functions exercise 2.1 question 5 sub question (xv)

Answers (1)

Bijective

Hint:

f:R \rightarrow R, defined by f(x)=3-4x.

Hint:

Bijective function should be one-one and onto function.

Solution:

Let  

\begin{aligned} &x_{1}, x_{2} \in R \\ &f\left(x_{1}\right)=3-4 x_{1}, f\left(x_{2}\right)=3-4 x_{2} \\ &f\left(x_{1}\right)=f\left(x_{2}\right) \\ &3-4 x_{1}=3-4 x_{2} \\ &x_{1}=x_{2} \end{aligned}

Hence f  is an injective.

Subjection test:

Let 

 \begin{aligned} &y=3-4 x\\ &x=\frac{3-y}{4}\\ &\therefore\\ &\forall y \in R, \exists \frac{3-y}{4} \in R\\ &f\left(\frac{3-y}{4}\right)=3-4\left(\frac{3-4}{4}\right)=y \end{aligned}

\therefore f is onto

Hence, f is bijection.

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