Question

Find the different quotient of f

Answer 1

2x + h - 5

Explanation:

To find f(x + h) we simply plug (x + h) into the function f(x), anywhere we see an x.

`f(x) = x^(2) -5x+9\\f(x+h) = (x+h)^(2)-5(x+h)+9`

Now we can plug them into the fraction:

`(((x+h)^(2)-5(x+h)+9)-(x^(2) -5x+9))/(h)`

Expanding all of the terms, we get:

`((x^(2) +2hx + h^(2) -5x-5h+9)-(x^(2) -5x+9))/(h)`

Distributing the negative we get:

`(x^(2) +2hx + h^(2) -5x-5h+9-x^(2) +5x-9)/(h)`

Now we see that
`x^(2) -x^(2) ,-5x+5x,` and
`9-9` all cancel, leaving us with:

`(2hx + h^(2)-5h)/(h)` (Notice the only terms left are those with h in them)

As every term contains an h, we can remove an h from every term, giving us:

2x + h - 5