Help with domain question with g(f(x))

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SUMMARY

The domain of the composite function g(f(x)), where f(x) = √x and g(x) = √(x² + 1), is determined by the inner function f(x). Since f(x) = √x is defined for x ≥ 0, the domain of g(f(x)) is also restricted to x ≥ 0. Therefore, the correct domain of g(f(x)) is [0, +∞).

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Homework Statement



If f(x)=√x and g(x)=√(x^2+1) what is the domain of g(f(x))?


The Attempt at a Solution



I cam up with (-∞,+∞) since the square root of a square is always positive, am I missing something here?
 
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