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44 votes
If f(x) =(4x^2 -11)^3 and g(x) = 4x^2 -11. given that f(x) = (h°g)(x) find h(x)

User Djthoms
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1 Answer

10 votes
10 votes

Given:


\left(x\right)=\left(4x^2-11\right)^3andg\left(x\right)=4x^2-11.

Required:

Find h(x) if


f\mleft(x\mright)=h°g\left(x\right)

Step-by-step explanation:


\begin{gathered} f\mleft(x\mright)=h°g\left(x\right) \\ f\mleft(x\mright)=h(g(x)) \end{gathered}

Let g(x) = x


f(x)=h(x)
(4x^2-11)^3=x^3

Solve by taking cube root on both sides.


x=4x^2-11
\begin{gathered} g(x)=x \\ g(x)=4x^2-11 \end{gathered}

User Soenke
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2.7k points