If f(x) = sqrt(x) and g(x) = x^2, what is the domain of f(g(x))?

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Master the Praxis Mathematics (5165) Test. Enhance your skills with flashcards and practice questions, each with detailed explanations. Ace your exam confidently!

Multiple Choice

If f(x) = sqrt(x) and g(x) = x^2, what is the domain of f(g(x))?

Explanation:
When composing functions, the input must make the inner function’s output fall inside the outer function’s domain. The outer function f is defined for inputs ≥ 0. Since g(x) = x^2 is always nonnegative for any real x, every real x makes g(x) fall inside f’s domain. Therefore, the domain of the composition is all real numbers, (-∞, ∞). You can also see this by noting f(g(x)) = sqrt(x^2) = |x|, which exists for every real x.

When composing functions, the input must make the inner function’s output fall inside the outer function’s domain. The outer function f is defined for inputs ≥ 0. Since g(x) = x^2 is always nonnegative for any real x, every real x makes g(x) fall inside f’s domain. Therefore, the domain of the composition is all real numbers, (-∞, ∞). You can also see this by noting f(g(x)) = sqrt(x^2) = |x|, which exists for every real x.

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