Given $$ f(x)=\sqrt{x} $$ and $$ g(x)=x^{2}+1 $$ What is the value of $$ (f \circ g)(\sqrt{3}) $$ ?

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To find the value of $$ (f \circ g)(\sqrt{3}) $$, we first need to understand what $$ (f \circ g)(x) $$ means. The notation $$ (f \circ g)(x) $$ represents the composition of the functions $$ f $$ and $$ g $$, which can be expressed as:

$$
(f \circ g)(x) = f(g(x))
$$

Now, we will first calculate $$ g(\sqrt{3}) $$.

Given $$ g(x) = x^2 + 1 $$, we substitute $$ x = \sqrt{3} $$:

$$
g(\sqrt{3}) = (\sqrt{3})^2 + 1 = 3 + 1 = 4
$$

Next, we need to evaluate $$ f(g(\sqrt{3})) $$, which is $$ f(4) $$.

Given $$ f(x) = \sqrt{x} $$, we substitute $$ x = 4 $$:

$$
f(4) = \sqrt{4} = 2
$$

Thus, the value of $$ (f \circ g)(\sqrt{3}) $$ is:

$$
\boxed{2}
$$
$$ (f \circ g)(\sqrt{3}) = 2 $$

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