Discussion

Explanation:

f(x + xy) = f(x) + f(xy)

Substituting y = 1
⇒ f(x + x) = f(x) + f(x)
⇒ f(2x) = 2f(x)

Substituting y = 2
⇒ f(x + 2x) = f(x) + f(2x)
⇒ f(3x) = f(x) + 2f(x)
⇒ f(3x) = 3f(x)

Hence, we can say, f(ax) = a × f(x)   ...(1)

Substituting a = 2020 and x = 1
⇒ f(2020) = 2020 × f(1)
⇒ 1 = 2020 × f(1)
⇒ f(1) = 1/2020

Now, putting x = 1 and a = 2021 in (1) we get,
f(2021) = 2021 × f(1) = 2021/2020

Hence, option (a).

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