Discussion

Explanation:

If f(x² + f(y)) = xf(x) + y for all non-negative integers x and y, then the value of [f(0)]² + f(0) equals _________.

Given, f(x² + f(y)) = xf(x) + y

Subsituting x = 1 and y = 0, we get

f(1 + f(0)) = f(1)

Now, if f(x) = f(y) it implies that x = y

Hence, 1 + f(0) = 1

⇒ f(0) = 0

∴ [f(0)]² + f(0) = [0]² + 0 = 0

Hence, option (b).

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