Question

1. choose the best answer. when we compose functions, we must make sure that the output of the first function is part of the _ of the second function. graph output domain range 2) choose the best answer. in general, the composition of functions is not _. associative commutative transitive identifiable 3) choose the best answer. we expect to see a ___ for the graph of a composition of a function and its inverse function, if the domain of each is all real numbers. line parabola curve circle

Explanation:

1. For function composition \(f(g(x))\), the output of \(g(x)\) must be in the domain of \(f(x)\) since the domain is the set of input - values for a function.
2. Function composition \(f(g(x))\) is not commutative in general. That is, \(f(g(x))

eq g(f(x))\) because the order of applying functions matters.

1. If \(y = f(x)\) and \(y = f^{-1}(x)\) and the domain of each is all real numbers, then \(f(f^{-1}(x))=x\) and \(f^{-1}(f(x)) = x\), and the graph of \(y = x\) is a line.

Answer:

1. C. domain
2. B. commutative
3. A. line