Question

1. what does it mean when f(x) = g(x) = h(x)?

Explanation:

The notation \( f(x) = g(x) = h(x) \) means that for a given input \( x \) (in the domain common to all three functions \( f \), \( g \), and \( h \)), the output of the function \( f \) at \( x \), the output of the function \( g \) at \( x \), and the output of the function \( h \) at \( x \) are all equal. In other words, \( f(x)=g(x) \) and \( g(x) = h(x) \) (and by the transitive property of equality, \( f(x)=h(x) \)) for that particular value of \( x \). This can imply that the graphs of the functions \( f \), \( g \), and \( h \) intersect at the point(s) corresponding to those \( x \)-values (if we are considering real - valued functions and their graphs in the coordinate plane), or more generally, that the functions have the same value at those specific \( x \)-values.

Answer:

It means that for a given \( x \) (in the common domain of \( f \), \( g \), and \( h \)), \( f(x)=g(x) \) and \( g(x) = h(x) \) (so \( f(x)=h(x) \) as well), i.e., the three functions have the same output at that \( x \)-value.