Basic Alegbra Questions.?

Question

The difference quotient for F(x)= x^2-5x+8

and also...

prove that f(x)=x^3-5x is an odd function. I remember you replace all the x's with negative x's, but that would change -5x to 5x and I dont know if that means its still an odd function.

Answer 1

The first bit - "The difference quotient for F(x)= x^2-5x+8" - is not a question.

The second bit: You are right, replace x with -x and you get:

f(-x) = (-x)^3 -5(-x)

= -x^3 + 5x

= -(x^3 -5x)

= -f(x)

So hence it is an odd function.

A function is odd if f(-x) = -f(x).

A function is even if f(-x) = f(x).