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

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

Answers (1)

Bijective.

Given:

As f:Z \rightarrow Z  defined by f(x)=x-5

Hint:

One-one function means every element in the domain has a distinct image in the  co-domain.

Onto function means every element in the co-domain has at least one  pre image in the domain of function.

Bijection ⇒ Function should fulfill the injection, surjection condition.

Solution:

Injection test:

Let x,y be any two elements in domain(Z)  such that f(x)=(y),f(x)=x-5,f(y)=y-5

f(x)=f(y)

x-5=y-5

x=y

So, f  is an injection.

Surjection test:

Let y be any element in the co-domain(Z)  such that  f(x)=y for some element x  in Z( domain)

f(x)=y

x-5=y   

x=y+5  which is in Z.

So, Z is a surjection and f is a bijection.

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