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.