What is f(0) equal to?
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.
- A. 0
- B. 1
- C. 5
- D. 10 ✓
Correct Answer: D. 10
Explanation
The relation f(xy)=f(x+y) is valid for all real x and y. Let x=0, then f(0\cdot y) = f(0+y) \implies f(0) = f(y). This shows that f(y) is a constant function for all y. Since f(5) = 10, the constant value is 10. Thus, f(0) = 10.
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