Functional notation confusing.

[AmySaunders]

Given f(x)=2/x solve this equation: f(x+h)-f(x)/h.

It looked just like a regular notation problem, but I cannot understand what you do to get rid ofthe denominator in all the areas of the problem. This problem is in my calculus book, nd the answer book says that the answer is 2/x(x+h)

Any and all help will be appreciated!

[AmySaunders]

Sorry, here are my steps:

[2/(x+h)]-(2/x)
___________________
h

Simplify:

(2/x)+(2/h)-(2/x)
__________________
h

Simplify again:

(2/h)
_____
h

Since you don't want to divide by a fraction, multiply by the reciprocal:

(2h/h)

You can cancel out the H and come out with 2, whcih is what I got. The answer book says it's wrong though, and I don't understand what to do.

[AmySaunders]

I can do the problems that have only one thing in f(x). Example:

Given: F(x)=2x^2 solve f(x+h)-f(h)/h

this problem I am okay with, but when it comes to fractions in functional notation I am stumped. Please help!

[stapel_eliz]

[2/(x+h)]-(2/x)
___________________
h

Simplify:

(2/x)+(2/h)-(2/x)
__________________
h

You can't do that.

You cannot split the denominator; you can only split the numerator. If you'd had (x + h)/2, you could have split this as x/2 + h/2, but it doesn't work the same way with denominators!

You need to start by finding the common denominator.

[AmySaunders]

So I find the common denominator in the numerator, and then what do I do?

Do I multiply the 2/x by h? Because if I do then i get a xh in the denominator and I don't know what to do!
You can't really get x+h in the denominator because you can't really add h to the numerator and the denominator. Or can you?

[AmySaunders]

I'm sorry to be so thick. Can we start over?

f(x)=2/x and (f(x+h)-f(x))/h

so I sub the second equation into the first, right?

And end up with 2h/((x+h)-x), which must not be right... because solved algebraically it does NOT give me the right answer. So I need help with the very first step, I think.

Thank you!

[stapel_eliz]

f(x)=2/x and (f(x+h)-f(x))/h

so I sub the second equation into the first, right?

I'm sorry, but I don't know what this means...?

Try plugging "x + h" in for "x" in the formula for "f(x)". Simplify. From the result, subtract f(x). Simplify. Then divide by h.

And end up with 2h/((x+h)-x)

How?

Please reply showing your steps. Thank you.