Question

I need to find the domain of the composite function g(f(x) for f(x)= x^2+1 and the square root of x-1.

Answer 1

\(g(x) = \sqrt{x-1}\) demands \(x \ge 1\)

\(f(x) = x^{2} + 1\) provides \(f(x) \ge 1\)

Seems like a perfect match.

\(f(x) = x^{2} + 1\) demands nothing: \(x \in \mathbb{R}\)

Answer 2

Thanks