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

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muriyabi muriyabi · Answer 1 · 2019-09-04T01:58:19+02:00

Answer:

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

(f/g)(x)= [tex]\frac{18x3-7x2+5x-3}{-9x2-2}[/tex], ∀ x / -9x2-2≠0

-9x2-2=0 → 9x2=-2 → x2=-[tex]\frac{9}{2}[/tex] → 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.

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carlosego carlosego · Answer 2 · 2019-09-04T03:09:47+02:00

For this case we have the following functions:

[tex]f (x) = 18x ^3-7x^2 + 5x-3\\g (x) = - 9x ^ 2-2[/tex]

We must find [tex](\frac {f} {g}) (x)[/tex]. By definition we have to:

[tex](\frac {f} {g}) (x) = \frac {f (x)} {g (x)}[/tex]

So:

[tex](\frac {f} {g}) (x) = \frac {18x ^ 3-7x ^ 2 + 5x-3} {- 9x ^ 2-2}[/tex]

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

That is to say:

[tex]-9x ^ 2-2[/tex] other than 0.

ANswer:

[tex](\frac {f} {g}) (x) = \frac {18x ^ 3-7x ^ 2 + 5x-3} {- 9x ^ 2-2}[/tex]

With[tex]-9x ^ 2-2[/tex] other than 0