Find the domain of the composite function (G(F(X)).

Question

F(X) = 3x      G(Y) = 1/Y

G(F(X)) = 1/3x

Answer 1

G(F(x)) = 1/3x

           =(1/3)(1/x)

First set the denominator equal to zero. Remember, dividing by 0 is undefined.

So if we find values of x that make the denominator zero, then we must exclude them from the domain.

The domain of the function

f(x) = 1/3x is all real numbers except zero (since at x = 0, the function is undefined: division by zero is not allowed!).

Domain: {x | x ∈ R, x ≠ 0}