Question

A function operation

Answer 1

if \[F(x)=\frac{ 1 }{ x }\]
find and express its simplest form:
\[\frac{ f(a+h)-f(a) }{ h }\]

Answer 2

That's all I have, what should I do?

Answer 3

You should get -1/ (a(a+h))

Answer 4

\[(\frac{ 1 }{ a+h }-\frac{ 1 }{ a }) \div h\]

Answer 5

Like that?

Answer 6

I'll start you off..........

Given: f(x) = 1/x

So, f(a+h) = 1/(a+h)
and f(a) = 1/a

So the expression you typed above is just:
[ (1/(a+h) - 1/a] /h

When you simplify that complex fraction above (not hard at all), you get -1/[a(a+h)] as your final answer.

Answer 7

Yes, like that!

Answer 8

Can you explain how did you simplify, please?

Answer 9

Let's take the numerator........

1/(a+h) - 1/a

To subtract, you get the LCD which is a(a+h),
so

1/(a+h) - 1/a = [a-(a+h)]/a(a+h)
= -h/(a(a+h))

Now, the denominator is just h, so you get

-h/(a(a+h)) divided by h/1 = -1/(a(a+h))

Answer 10

makes sense?

Answer 11

yep, thanks

Answer 12

welcome.

Answer 13

I had a silly math confusion