The process of combining two functions by using the output of one as the input of the other, denoted f(g(x)).

• A. Inverse
• B. Composition of functions
• C. Domain restriction
• D. Range

Answer: (B)

The idea being tested is composing functions. In f(g(x)), you first compute g(x), then use that result as the input to f. It’s like chaining two processes: the output of the first becomes the input to the second. The order matters—f(g(x)) generally differs from g(f(x)) because you’re feeding the functions into each other in a different sequence. For example, if g(x) = x + 3 and f(x) = 2x, then f(g(x)) = 2(x + 3) = 2x + 6, while g(f(x)) = 2x + 3. Also, the composite’s domain consists of all x for which g(x) lies in the domain of f, which can be a narrower set than the domain of g alone. Inverse refers to undoing a function, domain restriction is about limiting inputs, and range is about the outputs a function can produce—none describe the process of nesting one function inside another.