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Comprehension

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

What is f(0) equal to?

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NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
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  1. 0
  2. 1
  3. 5
  4. 10

Answer (Detailed Solution Below)

Option 4 : 10
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Detailed Solution

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Calculation:

Given,

The function is such that: for all real values of x  and y , and .

We need to find the value of .

Substitute and in the given functional equation :

Since , we conclude:

Hence, the correct answer is Option 4. 

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