Question
Express the given function \( h \) as a composition of two functions \( f \) and \( g \) so that \( h(x)=(f \circ g)(x) \), where one of the functions is \( 6 x-2 \). \( h(x)=(6 x-2)^{7} \) \( f(x)=\square \)
Ask by Cox Schultz. in the United States
Mar 17,2025
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Answer
\( f(x) = x^7 \)
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To express the function \( h(x) = (6x - 2)^7 \) as a composition of two functions \( f \) and \( g \), we can let \( g(x) = 6x - 2 \). Then, the second function \( f(x) \) will be \( f(x) = x^7 \). Therefore, we have: \[ h(x) = (f \circ g)(x) = f(g(x)) = f(6x - 2) = (6x - 2)^7 \] So, \( f(x) = x^7 \) works perfectly!