SOLUTION: Let f(x)=x2+x and g(x)=x+1. Find each of the following: (f+g)(x) (f.g)(x) (f divided by (g)(x)

Question 30566: Let f(x)=x2+x and g(x)=x+1. Find each of the following:
(f+g)(x) (f.g)(x) (f divided by (g)(x)
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
f(x)=x^2+x ----(1)
g(x)=x+1 ----(2)
Both (1) and (2) are defined for all real x
To find (f+g)(x) (f.g)(x) (f divided by (g)(x)
1) (f+g)(x) = f(x)+g(x)
= (x^2+x)+(x+1) using (1) and (2)
=x^2+(x+x)+1
= x^2+2x+1
2)(f.g)(x) = f(x).g(x)
= (x^2+x)(x+1) using (1) and (2)
=x^2(x+1)+x(x+1)
= (x^3+x^2)+(x^2+x)
= x^3+(x^2+x^2)+x
=x^3+2x^2+x
3)(f/g)(x) = f(x)/g(x) (for g(x) not zero)
= (x^2+x)/(x+1) [defined for x not equal to (-1)]
= x(x+1)/(x+1) (for x not equal to (-1))
= x (cancelling (x+1) not zero )

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