If $$ f(x)=x^{4}+6, g(x)=x-4, h(x)=\sqrt{x} $$, then $$ f \circ g \circ h(x)= $$

Question

UpStudy AI · Accepted Answer

To find $$ f \circ g \circ h(x) $$, we'll compose the functions step by step:

1. **Start with $$ h(x) $$:**
   $$
   h(x) = \sqrt{x}
   $$

2. **Apply $$ g $$ to $$ h(x) $$:**
   $$
   g(h(x)) = g(\sqrt{x}) = \sqrt{x} - 4
   $$

3. **Finally, apply $$ f $$ to $$ g(h(x)) $$:**
   $$
   f(g(h(x))) = f(\sqrt{x} - 4) = (\sqrt{x} - 4)^4 + 6
   $$

So, the composite function $$ f \circ g \circ h(x) $$ is:

$$
f \circ g \circ h(x) = (\sqrt{x} - 4)^4 + 6
$$

**Final Answer:**
$$
f \circ g \circ h(x) = \left( \sqrt{x}\; -\;4 \right)^4 + 6
$$
$$ f \circ g \circ h(x) = (\sqrt{x} - 4)^4 + 6 $$

If \( f(x)=x^{4}+6, g(x)=x-4, h(x)=\sqrt{x} \), then \( f \circ g \circ h(x)= \)