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)?

Answer 1

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:

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