Questions: Given that g(x)=x^5, find (g ∘ g)(x). (g ∘ g)(x)= (Simplify your answer.)

Transcript text: Given that $\mathrm{g}(\mathrm{x})=\mathrm{x}^{5}$, find $(\mathrm{g} \circ \mathrm{g})(\mathrm{x})$. $(g \circ g)(x)=$ $\square$ (Simplify your answer.)

Solution

Solution Steps

Step 1: Define the Function

We start with the function defined as $ g(x) = x^5 $.

Step 2: Find the Composition

To find $ (g \circ g)(x) $, we substitute $ g(x) $ into itself: \[ (g \circ g)(x) = g(g(x)) = g(x^5) \]

Step 3: Simplify the Expression

Now we apply the function $ g $ to $ x^5 $: \[ g(x^5) = (x^5)^5 = x^{25} \]

Final Answer

Thus, the simplified expression for $ (g \circ g)(x) $ is: \[ \boxed{x^{25}} \]

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