Respuesta :

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[tex]f(x)=x^2-x^3+x^2=x^2(x^2-x+1)\\\\g(x)=-x^2\\\\\left(\dfrac{f}{g}\right)(x)=\dfrac{x^2(x^2-x+1)}{-x^2}=-x^2+x-1[/tex]

Answer:

[tex]-x^2+x-1[/tex]

Step-by-step explanation:

Given functions are,

[tex]f(x) = x^4 - x^3 + x^2[/tex]

[tex]g(x) = -x^2[/tex]

Since,

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

[tex]=\frac{x^4-x^3+x^2}{-x^2}[/tex]

[tex]=-\frac{x^2(x^2-x+1)}{x^2}[/tex]

[tex]=-(x^2-x+1)[/tex]

[tex]=-x^2+x-1[/tex]

Hence, the value of (f/g)(x) is [tex]-x^2+x-1[/tex]

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