Domain of g(f(x)) where f(x) = sqrt(x) and g(x) = x^2?

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Multiple Choice

Domain of g(f(x)) where f(x) = sqrt(x) and g(x) = x^2?

Explanation:
When forming g∘f, you must ensure the inner output can be fed into the outer function. Here, f(x) = sqrt(x) requires x ≥ 0, so its outputs are nonnegative numbers. The outer function g(t) = t^2 accepts any real input, so it easily handles these nonnegative outputs. Therefore, no further restriction comes from g, and the domain is simply x ≥ 0, i.e., [0, ∞).

When forming g∘f, you must ensure the inner output can be fed into the outer function. Here, f(x) = sqrt(x) requires x ≥ 0, so its outputs are nonnegative numbers. The outer function g(t) = t^2 accepts any real input, so it easily handles these nonnegative outputs. Therefore, no further restriction comes from g, and the domain is simply x ≥ 0, i.e., [0, ∞).

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