Please help with an explanation!
For f(x) = 3x^2 - x - 2, find (f(x) - f(2))/(x-2)

Question

Please help with an explanation! 
For f(x) = 3x^2 - x - 2, find (f(x) - f(2))/(x-2)

legomyego180 · Answer

Hello are you there?

lynn.caroline · Answer

Yes

legomyego180 · Answer

$$f(x)=3x^2-x-2$$

The best way to start this is by defining everything the equation is asking us to find.

This is sort of a confusing question as well, its not asking for an answer, it just wants you to rewrite the equation.

lynn.caroline · Answer

So it doesn't want a real answer? How would I even got about rewriting the equation?

legomyego180 · Answer

$$\frac{ f(x)-f(2) }{ x-2 }$$

Lets define f(x)...the problem says:

$$f(x)=3x^2-x-2$$

So we can replace that into the function we are asked to find:

$$\frac{ (3x^2-x-2)-f(2) }{ x-2 }$$

Now we need to define f(2). To do this we just plug 2 in for everywhere there is an x in f(x):

$$f(x)=3x^2-x-2$$
$$f(2)=3(2)^2-2-2=8$$

We can now plug in 8 for f(2):
$$\frac{ (3x^2-x-2)-8 }{ x-2 }$$

Simplify:

$$\frac{ 3x^2-x-10 }{ x-2 }$$

lynn.caroline · Answer

So would the final answer be 3x+5?

legomyego180 · Answer

Yup!

legomyego180 · Answer

Good job. I forgot to factor the numerator.