F is Continuous or not?

Calculus Level 4

Let
f ( x ) = { 2 x 2 ; if x is rational 0 ; if x is irrational \large \color{#0C6AC7}{f(x)} = \begin{cases}\color{#D61F06}{ 2x^2 }&&;&& \text{if x is rational} \\ \color{#EC7300}{0} &&;&&\text{if x is irrational} \end{cases}
Then,

f f is continuous at infinitely many points of R R , but not all of R R f f is not continuous except at x = 0 x = 0 f f is continuous on all of R R None of these

Akhil Bansal by Akhil Bansal , 22, India

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