Question

If f(x) = x4 − x3 + x2 and g(x) = −x2, where x ≠ 0, what is (f ⁄g)(x)

Answer 1

Answer:

$-x^2+x-1$

Step-by-step explanation:

Given functions are,

$f(x) = x^4 - x^3 + x^2$

$g(x) = -x^2$

Since,

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

$=\frac{x^4-x^3+x^2}{-x^2}$

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

$=-(x^2-x+1)$

$=-x^2+x-1$

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

Answer 2

$f(x)=x^2-x^3+x^2=x^2(x^2-x+1)\\\\g(x)=-x^2\\\\\left(\dfrac{f}{g}\right)(x)=\dfrac{x^2(x^2-x+1)}{-x^2}=-x^2+x-1$