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

User Fifth
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1 Answer

5 votes

Answer:


(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

User Nathen
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