Question

Evaluate the function (f/g)(-1)-g(3) for f(x)=x^2+1 and g(x)=x-4

Answer 1

`(f/g)(-1)-g(3)=(f(-1))/(g(-1))-g(3) \\ \\ f(x)=x^2+1 \\ f(-1)=(-1)^2+1=1+1=2 \\ g(x)=x-4 \\ g(-1)=-1-4=-5 \\ g(3)=3-4=-1 \\ \\ (f(-1))/(g(-1))-g(3)=(2)/(-5)-(-1)=-(2)/(5)+1=(3)/(5) \\ \\ \boxed{(f/g)(-1)-g(3)=(3)/(5)}`