Question

For the functions f(x)=x4−x3−7x2+9x−2 and g(x)=x−1, find (f/g)(x) and (f/g)(2).

Answer 1

`(f/g)(x)=(x^4-x^3-7x^2+9x-2)/(x-1) =x^3-7x+2\,\,\,for\,\,x\\eq 1`

`(f/g)(2)=-4`

Explanation:

`(f/g)(x)=(x^4-x^3-7x^2+9x-2)/(x-1) =x^3-7x+2\,\,\,for\,\,x\\eq 1` and undefined for x = 1.

Notice that (x-1) is in fact a factor of f(x), so the quotient of the two functions introduces a "hole" for the new function at x = 1.

f(2) can be found by simply evaluating the expression for x = 2:

`(f/g)(2)=2^3-7(2)+2=-4`