Question

Given f(X)= 2x-5 and g(X) = x^2-3x which of the following is the domain of f(g(X))?

Answer 1

First, let's calculate the composite function f(g(x)):

$\begin{gathered} f(x)=2x-5 \\ g(x)=x^2-3x \\ \\ f(g(x))=2(x^2-3x)-5 \\ f(g(x))=2x^2-6x-5 \end{gathered}$

Since the function is a quadratic polynomial and there are no fractions or square roots, so the domain of this function is all real numbers, that is, (-infinity, infinity).