For this case we have the following functions:
[tex]f (x) = x ^ 4-x ^ 3 x ^ 2\\g (x) = - x ^ 2[/tex]
By definition of composition of functions we have to:[tex](f \ g) (x) = \frac {f (x)} {g (x)}[/tex]
So:
[tex]\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} =[/tex]
By definition of division of powers of the same base we have to place the same base and subtract the exponents:
[tex]\frac {f (x)} {g (x)} = - x ^ 2+x-1[/tex]
ANswer:
[tex](\frac {f} {g}) (x) = - x ^ 2 +x-1[/tex]
