\[
f(x)=\sqrt{x-1} \text { and } g(x)=x^{3}+4
\]

Step 2 of 2 : Find the formula for $(g \circ f)(x)$ and simplify your answer.
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Answer

The formula for $g \circ f(x)$ is $\boxed{(\sqrt{x-1})^3 + 4}$ or $\boxed{(x - 1)^{3/2} + 4}$.

Steps

Step 1 ：Given the functions $f(x)=\sqrt{x-1}$ and $g(x)=x^{3}+4$.

Step 2 ：We need to find the formula for $g \circ f(x)$, which means we substitute $f(x)$ into $g(x)$.

Step 3 ：Substitute $f(x)$ into $g(x)$, we replace $x$ in $g(x)$ with $\sqrt{x-1}$ to get $g \circ f(x) = (\sqrt{x-1})^3 + 4$.

Step 4 ：Simplify the expression to get the final answer.

Step 5 ：The formula for $g \circ f(x)$ is $\boxed{(\sqrt{x-1})^3 + 4}$ or $\boxed{(x - 1)^{3/2} + 4}$.