For $$ f(x)=x^{11} $$ and $$ g(x)=\sqrt[11]{x} $$, find $$ (f \circ g)(x) $$ and $$ (g \circ f)(x) $$. Then determine whether $$ (f \circ g)(x)=(g \circ f)(x) $$ of 3 What is $$ (f \circ g)(x) $$ ? $$ (f \circ g)(x)=\square $$

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UpStudy AI · Accepted Answer

We have 
$$
f(x)=x^{11} \quad \text{and} \quad g(x)=\sqrt[11]{x}=x^{\frac{1}{11}}.
$$

**Step 1: Compute $$(f \circ g)(x)$$**

By definition,
$$
(f \circ g)(x)=f(g(x)).
$$
Substitute $$ g(x)=x^{\frac{1}{11}} $$ into $$ f(x) $$:
$$
f(g(x))=\left(x^{\frac{1}{11}}\right)^{11}.
$$

**Step 2: Simplify the expression**

Using the power of a power rule, $$\left(x^{\frac{1}{11}}\right)^{11}=x^{\frac{11}{11}}=x^1=x$$.

**Final Answer:**
$$
(f \circ g)(x)=x.
$$

$$\boxed{x}$$
$$(f \circ g)(x) = x$$

For and , find and . Then determine whether of 3
What is ?

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