KCET2013MathematicsContinuity and Differentiability

If f(x)= array ll x, & if x is irrational 0, & if x is rational array . , then f is

Options

Acontinuous everywhere
Bdiscontinuous everywhere
Ccontinuous only at x=0
Dcontinuous at all rational numbers

Correct answer

C. continuous only at x=0

Step-by-step solution

Given, f(x)= cases x, & if x is irrational 0, & if x is rational cases aligned & LHL = _ x 0⁻ f(x)= _ x 0⁻ x=0 & RHL = _ x 0⁺ f(x)= _ x 0⁺ x=0 aligned and f(0)=0 Hence, f(x) is continuous at x=0 .

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