Question

If f(x + y) = f(xy) ∀ x, y ∈ R then prove that f is a constant function.

Answer 1

Thank you for asking this question. Here is your answer:

First of all we will let x be any real

and y will be equal to 0.

Then we will assume the following values:

f(x+0) = f(x*0)

In order to find out the final answer:

So f(x) = f(0) for all real x.

So we know that the function is a constant function.

If there is any confusion please leave a comment below.

Answer 2

Answer:

f is a constant function.

Step-by-step explanation:

It is given that f(x + y) = f(xy) for all x, y ∈ R   ---- (i)

Taking y = 0 in (i), we obtain

f(x + 0) = f(x * 0)

f(x) = f(0).

Hence,it is proved that f is a constant function.

Hope it helps!