Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What operation does (f ° g)(x) represent?

g(f(x))
f(g(x))
f(x) + g(x)
g(x) - f(x)

The correct answer is: f(g(x))

The notation (f ° g)(x) signifies the composition of two functions, which means that you apply one function to the result of another. Specifically, (f ° g)(x) indicates that you first evaluate the function g at x and then use that result as the input for the function f. This is mathematically represented as f(g(x)). To clarify, when you see (f ° g)(x), you can think of it as "f of g of x." You perform the operation of g on x to get g(x), and then you take that output and feed it into the function f. Therefore, the composition of functions results in f(g(x)), denoting a systematic process of chaining the functions together. This understanding underscores the core concept of function composition in mathematics, allowing you to evaluate complex operations by breaking them down into simpler steps.