Expert: Sherman D. - 3/18/2004

Question
Hi!  I talked to you yesterday about an equation I was having trouble with.  THanks so much for the process and the answer, but I need to know the background on those types of questions.  Can you explain thoroughly how you do them and why you do them that way? My textbook is very unclear about the how and why.  Thanks.  Here is another question of that type:

Q(x)=x^2-5x+1

{Q(2+h)-Q(2)}
    /h


Answer
if you know about f(x), where whatever x is, you have to replace x with that value.
For ex:
f(x) = 2x + 5, for x = 2
so we say this
f(2) = 2(2) + 5
f(2) = 4 + 5
f(2) = 9

so as for your problem

Q(x) = x^2 - 5x + 1
Q(2 + h) is saying that "x" is "2 + h"
and
Q(2) is saying that "x" is 2
So all you have to do is first replace "x" with "2 + h" for the Q(2 + h), and then replace "x" with "2" for the Q(2), but while still using the same equation that you are given.

In otherwords

Q(x) = x^2 - 5x + 1
Q(2 + h) = (h + 2)^2 - 5(h + 2) + 1
Q(2 + h) = ((h + 2)(h + 2)) - 5h - 10 + 1
Q(2 + h) = (h^2 + 2h + 2h + 4) - 5h - 9
Q(2 + h) = h^2 + 4h + 4 - 5h - 9
Q(2 + h) = h^2 - h - 5

and

Q(2) = (2)^2 - 5(2) + 1
Q(2) = 4 - 10 + 1
Q(2) = -5

so

{Q(2 + h) - Q(2)}/h

Becomes

{(h^2 - h - 5) - (-5)}/h

so you get

{h^2 - h - 5 + 5}/h

the "5"s cancel out, so this leaves you with

{h^2 - h}/h

one was is to go ahead and say that the answer is h - 1, or you can work it out mathematically

{(h^2)/h} - {h/h}

so you get the answer of h - 1

keep in mind when you have a problem like

f(x) and g(x), those are 2 different equations. Some problem will say that "x" is "n" where n is any value. So you substitute "n" in for "x" for both problems.

As for more info, just go to www.mywebsearch.com and type in functions and see what shows up.

Just keep the problems coming, making sure you type them so that i can understand them like you have done with this problem. And i will show you each step that is taken to solve the problems.