Pregunta
Express the function \( F \) in the form \( f_{\circ} g \). (Enter your answers as a comma-separated list. Use non-identity functions for \( f(x) \) and \( g(x) \). \[ F(x)=(x-7)^{5} \] \( (f(x), g(x))=(\square) \) Need Help? Watch It SUBMIT ANSWER
Ask by Reyes Harrington. in the United States
Mar 01,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( f(x) = x^5 \), \( g(x) = x - 7 \)
Solución
We want to express F(x) = (x – 7)⁵ as a composition f(g(x)). One simple way to do this is to let
f(x) = x⁵ and g(x) = x – 7.
Then, f(g(x)) = [g(x)]⁵ = (x – 7)⁵, which is exactly F(x).
Thus, one answer is: x⁵, x – 7.
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Simplifique esta solución The Deep Dive
To express the function \( F(x) = (x - 7)^{5} \) in the form of \( f_{\circ} g \), we can define two functions where \( g(x) \) is the inner function that simplifies the input to \( f(x) \). Let's choose \( g(x) = x - 7 \) and \( f(x) = x^{5} \). So, in the form of \( f_{\circ} g \), we have: \[ (f(x), g(x)) = (x^{5}, x - 7) \]
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