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  • Explain solution RD Sharma class 12 chapter Functions exercise 2.1 question 5 sub question (ix) maths

Explain solution RD Sharma class 12 chapter Functions exercise 2.1 question 5 sub question (ix) maths

Answers (1)

Bijective

Given:

f:R \rightarrow R   defined by f(x)=x^3+1.

Hint:

Bijection: function should be one-one and onto function.

Solution:

Injection test:

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

x^3+1=y^3+1

x^3=y^3

x=y

So, f is an injection.

Surjection test:

Let y be any element in the codomain (N) , such thatf(x)=y  for some element x in R .

f(x)=y

x^3 +1=y

x^3 =y-1

x=\sqrt[3]{(y-1)}\in R

So, f is a surjection.

So, f is a bijection.

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