QuestionJuly 14, 2025

Given that g(x)=x^4 , find (gcirc g)(x) (gcirc g)(x)=square (Simplify your answer.)

Given that g(x)=x^4 , find (gcirc g)(x) (gcirc g)(x)=square (Simplify your answer.)
Given that g(x)=x^4 , find (gcirc g)(x)
(gcirc g)(x)=square 
(Simplify your answer.)

Solution
4.5(191 votes)

Answer

x^{16} Explanation 1. Understand the Composition The composition (g \circ g)(x) means g(g(x)). 2. Substitute g(x) into Itself Since g(x) = x^4, substitute to get g(g(x)) = g(x^4). 3. Apply the Function Again Now, apply g(x) to x^4: g(x^4) = (x^4)^4. 4. Simplify the Expression Simplify (x^4)^4 using the power rule: **(a^m)^n = a^{m \cdot n}**. So, (x^4)^4 = x^{16}.

Explanation

1. Understand the Composition<br /> The composition $(g \circ g)(x)$ means $g(g(x))$.<br /><br />2. Substitute $g(x)$ into Itself<br /> Since $g(x) = x^4$, substitute to get $g(g(x)) = g(x^4)$.<br /><br />3. Apply the Function Again<br /> Now, apply $g(x)$ to $x^4$: $g(x^4) = (x^4)^4$.<br /><br />4. Simplify the Expression<br /> Simplify $(x^4)^4$ using the power rule: **$(a^m)^n = a^{m \cdot n}$**. So, $(x^4)^4 = x^{16}$.
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