If $$ f(x)=x^{4}+7, g(x)=x-1, h(x)=\sqrt{x} $$, then $$ f \circ g \circ h(x)=\square $$

Question

UpStudy AI · Accepted Answer

To find $$ f \circ g \circ h(x) $$, we need to compose the functions $$ f $$, $$ g $$, and $$ h $$ in the given order. Here's a step-by-step breakdown:

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

2. **Apply $$ g $$ to the result of $$ h(x) $$:**
   $$
   g(h(x)) = g(\sqrt{x}) = \sqrt{x} - 1
   $$

3. **Finally, apply $$ f $$ to the result of $$ g(h(x)) $$:**
   $$
   f(g(h(x))) = f(\sqrt{x} - 1) = (\sqrt{x} - 1)^4 + 7
   $$

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

$$
f \circ g \circ h(x) = (\sqrt{x} - 1)^4 + 7
$$

**Answer:**
After simplifying, the composition is (√x – 1)⁴ plus seven. Thus,

f ∘ g ∘ h (x) = (√x−1)^4 + 7
$$ f \circ g \circ h(x) = (\sqrt{x} - 1)^4 + 7 $$

If \( f(x)=x^{4}+7, g(x)=x-1, h(x)=\sqrt{x} \), then \( f \circ g \circ h(x)=\square \)

Solución de tutoría real

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Pre Calculus Questions