Question

Let f be a function satisifying f(xy) = f(x)/y for all positive real numbers x and y. if f(500) = 3, what is the value of f(600)?

Answer 1

Given that f(xy) = f(x)/y for any function f, and f(500) = 3, we find f(1) is 3/500. We then compute f(600) using f(1) to find that f(600) = 3.6.

Step-by-step explanation:

To find the value of f(600) given that for a function f satisfying the equation f(xy) = f(x)/y for all positive real numbers x and y, and knowing that f(500) = 3, we must relate the arguments 500 and 600. We will explore this relation by using the properties of the function.

First, we can find f(1) by setting x=500 and y=500, which gives us:
f(500) = f(500)/500, from which f(1) = 3/500. Then we can find f(600) by setting x=600 and y=1, which, using the found value of f(1), gives:
f(600) = f(600)/1 = f(1)×600 = (3/500)×600.

Now we can compute:
f(600) = (3/500)×600 = (3×600)/500 = 1800/500 = 3.6. Therefore, the value of f(600) is 3.6.