The "default" domain of a given "formula" is the largest set of numbers for which it can be calculted.
In order to be in the domain of a composition of functions, fog(x)= f(gx)), x must be in the domain of g and y= g(x) must be in the domain of f.
Here, and we can certainly square any real number, and then subtract 1. Any number is in the domain of f. which has domain all x such that . Okay, replacing that "x" with g(x) we are saying that . Can you solve ?
g o f(x) is comparatively easy- q has domain all real numbers so the domain of the composition is just the domain of f.
f o f(x) has domain is all x such that 3x- 8\ge 0 and .