SOLUTION: Help please! f(x)=3x^2-2x and g(X)=x-6 find each value for the below: 1: (f/g)(-1) 2: (gof)(3) 3: (fog)(0)

Question 402133: Help please!
f(x)=3x^2-2x and g(X)=x-6 find each value for the below:
1: (f/g)(-1)
2: (gof)(3)
3: (fog)(0)
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
1: (f/g)(-1)
this notation could be : (f o g^-1)(-1) or (g^-1 o f)(-1) but not defined as left or right multiplication by the inverse of g, hence we shall report the division on the real numbers for which the multiplication is commutative, and get :
f(-1)/g(-1) = (3-2*(-1))/(-1-6) = -5/7

(as for example, (f o g^-1)(-1) = 3*g^-1(-1)^2 - 2*g^-1(-1) and g^-1(x) = x+6, hence

(f o g^-1)(-1) = 3*(5)^2 - 2*5 = 3*25 - 10 = 75-10 = 65)

2: (gof)(3) = g(f(3))= f(3)-6 = 3*(3)^2-2*3-6 = 3*9-12 = 27-12 = 15

3: (fog)(0) = f(g(0)) = 3*g(0)^2-2*g(0) = 3*(-6)^2 -2*(-6) = 3*36 + 12

= 90 + 18 + 12 = 90 + 30 = 120
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