What does (fog)(x) denote?

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Study for the Algebra 1 Honors End-of-Course Test. Study with flashcards and multiple-choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

What does (fog)(x) denote?

Explanation:
Composition of functions means you apply one function to the result of another. The notation (fog)(x) is read as “f of g of x,” so you first compute g(x) and then feed that result into f. In other words, the value is f(g(x)). For example, if f(u) = u^2 and g(x) = 3x + 1, then (fog)(x) = f(g(x)) = (3x + 1)^2. If you plug in x = 2, you get g(2) = 7 and f(7) = 49, so (fog)(2) = 49. This is different from f(x) + g(x) or f(x)/g(x); those would combine the separate outputs in arithmetic ways, not pass the result of one function into the other.

Composition of functions means you apply one function to the result of another. The notation (fog)(x) is read as “f of g of x,” so you first compute g(x) and then feed that result into f. In other words, the value is f(g(x)).

For example, if f(u) = u^2 and g(x) = 3x + 1, then (fog)(x) = f(g(x)) = (3x + 1)^2. If you plug in x = 2, you get g(2) = 7 and f(7) = 49, so (fog)(2) = 49.

This is different from f(x) + g(x) or f(x)/g(x); those would combine the separate outputs in arithmetic ways, not pass the result of one function into the other.

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