if f(x) = x^4-x^3+x^2 and g(x)= -x^2, where x does not = 0, what is (f/g)(x)?

Question

if f(x) = x^4-x^3+x^2 and g(x)= -x^2, where x does not = 0, what is (f/g)(x)?

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Isabella 2 weeks 2021-09-09T08:12:32+00:00 1 Answer 0

Answers ( )

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    2021-09-09T08:14:06+00:00

    For this case we have the following functions:

    f (x) = x ^ 4-x ^ 3 x ^ 2\\g (x) = - x ^ 2

    By definition of composition of functions we have to:(f \ g) (x) = \frac {f (x)} {g (x)}

    So:

    \frac {f (x)} {g (x)} = \frac {x ^ 4-x ^ 3 x ^ 2} {- x ^ 2} = \frac {x ^ 4} {- x ^ 2} +\frac {-x ^ 3} {- x ^ 2}+ \frac {x ^ 2} {- x ^ 2} =

    By definition of division of powers of the same base we have to place the same base and subtract the exponents:

    \frac {f (x)} {g (x)} = - x ^ 2+x-1

    ANswer:

    (\frac {f} {g}) (x) = - x ^ 2 +x-1

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