Question

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

Answer 1

`-(h)/(x(x+h))`

Explanation:

Given:

`f(x)=(1)/(x)`

To find
`f(x+h)-f(x)`

Solution.

We will first find
`f(x+h)` by plugging in
`(x+h)` in place of
`x` in
`f(x+h)`

∴
`f(x+h)=(1)/(x+h)`

So,
`f(x+h)-f(x)`

⇒
`(1)/(x+h)-(1)/(x)`

Taking LCD as product of denominators as they are unknown variables.

Making the denominators common by multiplying the with corresponding terms.

⇒
`(1* x)/((x)(x+h))-(1* (x+h))/((x)(x+h))`

⇒
`(x)/((x)(x+h))-(x+h)/((x)(x+h))`

⇒
`(x-(x+h))/((x)(x+h))` [Subtracting the numerators]

⇒
`(x-x-h)/((x)(x+h))`

⇒
`(-h)/((x)(x+h))`

⇒
`-(h)/(x(x+h))` (Answer)