The sum of 2 positive numbers is 62. Write an equation that gives the product of the two numbers.

Question

What is the domain and range of this function?

Answer 1

x + y = 62

y = 62 - x

product:  xy = x(62-x)  and now you may call this (product) f(x) = x(62-x). 

 

The domain is (0,62) because otherwise the "both numbers are positive" requirement would be violated.

Thlus the range of f would be (0,y_max) where the y_maxwould be f(31) based on vertex of parabola opening downwardly.