1. state the domain of f(x)= x-2/x^2-x-6
2. given that f(x)=x^2+1 and g(x)= 3x+2, find all values of x such that f(g(x))= g(f(x))
3. if f(x)= x^3-3x^2-2x+5 and g(x)=2, fin the value of g(f(x))
1. The domain of a polynomial is in general ℝ. If a polynomial is divided by another, the zeroes of the denominator must be excluded from the domain, namely ℝ.
2. Find fog and gof, equate the two functions and solve for x.
3. Since g(x) is a constant function, we conclude that g(f(x))=2, as long as f(x) is defined on ℝ.