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

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

Answers (1)

Bijective

Given:

f:R \rightarrow R, defined by f(x)=5x^3+4

Hint:

Bijective function should be one-one and onto function.

Solution:

Let x  and y be any two elements in the domain(R), such that f(x)=f(y).

\begin{aligned} &\Rightarrow 5 x^{3}+4=5 y^{3}+4 \\ &\Rightarrow 5 x^{3}=5 y^{3} \\ &\Rightarrow x^{3}=y^{3} \\ &\Rightarrow x=y \end{aligned}

So, f is an injection.

Subjection test:

Let y be any element in the co-domain(R), such that f(x)=y.

\begin{aligned} &5 x^{3}+4=y \\ &x^{3}=\frac{(y-4)}{5} \in R \end{aligned}

So, f  is a surjective.

Hence, f  is a bijective.

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