Given the following: \( f(x)=\sqrt{x+3}, g(x)=3 x \), and \( h(x)=x^{2}-3 \) determine the solution to the following composition. \( f(h(x)) \) \( 3 \sqrt{x+3} \), as long as \( x \geq 0 \) \( \sqrt{3 x+3} \), as long as \( x \geq 0 \) \( x \), as long as \( x \geq 0 \) \( 3 x^{2}-3 \), as long as \( x \geq 0 \)

To find \( f(h(x)) \), we need to substitute \( h(x) \) into \( f(x) \). Starting with \( h(x) = x^2 - 3 \), we can replace \( x \) in \( f(x) = \sqrt{x + 3} \) with \( h(x) \): \[ f(h(x)) = f(x^2 - 3) = \sqrt{(x^2 - 3) + 3} = \sqrt{x^2} \] The square root of \( x^2 \) gives us \( |x| \). However, since we are given the constraint that \( x \geq 0 \), we can simplify this to just \( x \). Thus: \[ f(h(x)) = x \quad \text{as long as} \quad x \geq 0 \] Among the multiple choice answers provided, the correct one is: **\( x \), as long as \( x \geq 0 \)**.