What is f(20)+f(-20) equal to?

Question

Question

Consider the following for the two (02) items that follow:

A function f is such that f(xy) = f(x + y) for all real values of x and y, and f(5) = 10

This question was previously asked in

NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)

Answer 1

Calculation:

Given,

The function is \( f(xy) = f(x + y) \) for all real values of x and y, and f(5) = 10 .

We are tasked with finding:

\( f(20) + f(-20) \)

Using the given functional equation, we have:

For \( f(0 \cdot 5) = f(0 + 5) \), we get:

\( f(0) = f(5) = 10 \)

For \( f(0 \cdot 20) = f(0 + 20) \), we get:

\( f(0) = f(20) = 10 \)

For \( f(0 \cdot -20) = f(0 + (-20)) \), we get:

\( f(0) = f(-20) = 10 \)

Thus,

\( f(20) + f(-20) = 10 + 10 = 20 \)

Hence, the correct answert is Option 3.

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