i am not sure what I should do

[natalie45]

given f(x)=1/x , find f(x+h) - f(x)
h

i haven't done anything on the problem because i am confused on how to plug it in.

 

[srmichael]

given f(x)=1/x , find f(x+h) - f(x)
h

i haven't done anything on the problem because i am confused on how to plug it in.

You need to find \(\displaystyle \frac{f(x+h)-f(x)}{h}\) given \(\displaystyle f(x)=\frac{1}{x}\)

Let me ask you, if I asked you to find f(3), what would you do? Now, instead of "3" use "x + h". Does that make sense? Then proceed with the calculation asked for.

Take a stab at it then let us know what you got.

 

[Mrspi]

given f(x)=1/x , find f(x+h) - f(x)
h

i haven't done anything on the problem because i am confused on how to plug it in.

f(x) = 1/x

tells us that there is a function called "f" which takes an input called x, and produces an output in the form 1/x.

so, knowing that f(x) = 1/x, we also know that
f(n) = 1/n
and
f(a) = 1/a
and
f(5) = 1/5
and
f(x + 2) = 1/(x + 2)

So.....can you tell what f(x + h) is going to look like?

Does that help you do SOMETHING on this problem which you can show us? Then we can continue if you are still "stuck."

 

[needmathhelpnow]

Try

[{ 1 / (x + h) } - (1 / x) ] / h

then multiply both numerator and denominator by x(x+h)

the result is

(x - x - h) / [hx(x + h)]

the -h cancels with an h in the denominator and the final result is

-1 / x(x + h)

:-?

 

[pappus]

Try

[{ 1 / (x + h) } - (1 / x) ] / h

then multiply both numerator and denominator by x(x+h)

the result is

(x - x - h) / [hx(x + h)]

the -h cancels with an h in the denominator and the final result is

-1 / x(x + h)

:-?

Your result is correct!

There is only a small mistake in your comment: You didn't cancel out -h but h. Otherwise the negative sign had to be in the denominator.