Question

Let f(x) = x² - 1, g(x) = x³, and F(x) = (1) / (x - 2). Simplify the following expression. g(F(f(x))

Answer 1

The simplification of the expression g(F(f(x))) for given f(x) = x² - 1, g(x) = x³, and F(x) = (1) / (x - 2), results in ((1) / (x² - 3))³.

Step-by-step explanation:

The expression we need to simplify is g(F(f(x))). Before simplifying this expression, we have to evaluate f(x), which is given as x² - 1. We substitute this result into F(x), resulting in F(f(x)) = (1) / ((x² - 1) - 2) = (1) / (x² - 3). For the final simplification we then substitute this result into g(x), yielding g(F(f(x))) = ((1) / (x² - 3))³.The simplification of the expression g(F(f(x))) for given f(x) = x² - 1, g(x) = x³, and F(x) = (1) / (x - 2), results in ((1) / (x² - 3))³.

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