Determine a possible linear function f(x) such that x^2-x-2 < f(x)< x^3-x^2-2x has a solution and state the solution.(the < are supposed to have lines under that indicate less than/equal to)

Question

Determine a possible linear function f(x) such that x^2-x-2 < f(x)< x^3-x^2-2x has a solution and state the solution.(the < are supposed to have lines under that indicate less than/equal to)

I just don't really get what it's asking. So I factored each equation and they are (x+1)(x-2) and x(x+1)(x-2)

I just don't know how to proceed from there

Answer 1

There is no linear function which lies between the curves for all values of x.

See the graphs at

http://www.wolframalpha.com/input/?i=plot+x%5E2-x-2+,x%5E3-x%5E2-2x

If you restrict your domain, you can easily specify a line that lies between the curves on some interval.