Question

Is the following relation a function? Justify your answer 

(i) R₁ = {(2, 3), ( 1/2 , 0), (2, 7), (– 4, 6)} 

(ii) R₂ = {(x, |x |) | x is a real number}

Answer 1

(i) Since (2, 3) and (2, 7) ∈ R₁ 

⇒ R₁ (2) = 3 and R₁ (2) = 7 

So R₁ (2) does not have a unique image. Thus R₁ is not a function. 

(ii) R₂ = {(x, |x |) / x ∈R} For every x ∈ R there will be unique image as |x | ∈ R. 

Therefore R₂ is a function.