Simple Domain Question

[certainlyuncertain]

If f(x) = sqrt(x) and g(x) = x^2, is the domain of g(f(x)) still [0, inf), or is it (-inf, inf) because the new function n(x) simplifies to n(x) = x? I'm inclined to assume x must still be positive.

 

[stapel]

If f(x) = sqrt(x) and g(x) = x^2, is the domain of g(f(x)) still [0, inf), or is it (-inf, inf) because the new function n(x) simplifies to n(x) = x? I'm inclined to assume x must still be positive.

The domain of g(f(x)) has to rely on the domain on f(x), because you can't plug into f(x) things from outside of its domain. Because you're dealing with g(f(x)), rather than simply with g(x), you're working with what goes into f, not with what goes into g.

 

[Ishuda]

If f(x) = sqrt(x) and g(x) = x^2, is the domain of g(f(x)) still [0, inf), or is it (-inf, inf) because the new function n(x) simplifies to n(x) = x? I'm inclined to assume x must still be positive.

The domain of g(f(x)) is the range of f(x). Assuming sqrt(x) means the positive square root, the range of f(x) is [0,inf)