For the following two (02) items: Consider the function f(x) = x 1 - x ( x > 0 , x 1 ). What is f(x) f(x+1) equal to?

Step-by-step solution

Given f(x) = x 1 - x Substitute x+1 for x to find f(x+1) : f(x+1) = x+1 1 - (x+1) = x+1 -x Now, calculate the ratio f(x) f(x+1) : f(x) f(x+1) = x 1 - x x+1 -x f(x) f(x+1) = x 1 - x -x x+1 = -x^2 1 - x^2 Since f(x^2) = x^2 1 - x^2 , we get: f(x) f(x+1) = -f(x^2) Answer: -f(x^2)