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

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The problem involves finding the domain of the composite function g(f(x)), where f(x) = √x and g(x) = √(x^2 + 1). The initial assumption was that the domain is (-∞, +∞) due to the properties of square roots. However, upon further reflection, it was recognized that the domain of f(x) is restricted to x ≥ 0, as the square root function is only defined for non-negative values. Consequently, the domain of g(f(x)) is also limited to x ≥ 0, since g(f(x)) inherits the domain restrictions from f(x). The final conclusion clarifies that the 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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