Question

Find (f/g)(x) for the following functions. f(x)= 18x3 - 7x2 + 5x-3; g(x)= -9x2 -2

Answer 1

Step-by-step explanation: To find the function (f/g)(x) first we need to establish the limits as follows:

(f/g)(x)=
`(18x3-7x2+5x-3)/(-9x2-2)`, ∀ x / -9x2-2≠0

-9x2-2=0 → 9x2=-2 → x2=-
`(9)/(2)` → x=±√(9/2).

As we can see, the range of this function is ∀ x / x≠±√(9/2).

Becouse in those values, the function does´t have solution.

Answer 2

For this case we have the following functions:

`f (x) = 18x ^3-7x^2 + 5x-3\\g (x) = - 9x ^ 2-2`

We must find
`(\frac {f} {g}) (x)`. By definition we have to:

`(\frac {f} {g}) (x) = \frac {f (x)} {g (x)}`

So:

`(\frac {f} {g}) (x) = \frac {18x ^ 3-7x ^ 2 + 5x-3} {- 9x ^ 2-2}`

Where the denominator must be 0stint, so that the function is defined.

That is to say:

`-9x ^ 2-2` other than 0.

ANswer:

`(\frac {f} {g}) (x) = \frac {18x ^ 3-7x ^ 2 + 5x-3} {- 9x ^ 2-2}`

With
`-9x ^ 2-2` other than 0