Question 1

F(x)=x^2/3 and g(x)=sqrt(x-3)Find (f o g) (x) and (f o g)(4)

Question 2

SOLUTION:

Step 1 :

We are considering two equations:

$\begin{gathered} f(x)=x^{(2)/(3)} \\ \text{and } \\ g\text{ ( x ) = }\sqrt[]{x-3} \end{gathered}$

Step 2:

First, we are meant to find the formula for:

$(f^o\text{g)(x) and then we simplify our answer}$
$(f^og)(x)\text{ = f(g(x))}$
$\begin{gathered} (f^og)(x)\text{ = f(g(x))} \\ f(\sqrt[]{x-3}\text{ ) } \\ \text{but f ( x ) = x}^{(2)/(3)} \\ \text{Then, (f}\sqrt[]{x-3\text{ }})\text{ = (}\sqrt[]{x-3})^{(2)/(3)} \\ (f^og)(x\text{ ) = ( }\sqrt[]{x-3})^{(2)/(3)} \end{gathered}$

Step 3:

$\begin{gathered} \operatorname{Re}call\text{ that} \\ \\ (f^o\text{g)(x) =(}\sqrt[]{x\text{ - 3}})^{(2)/(3)} \\ (f^og)\text{ (4) = (}\sqrt[]{4-3})^{(2)/(3)} \\ =1^{(2)/(3)} \\ =\text{ 1} \\ \text{CONCLUSION:} \\ (f^og)(4)\text{ = 1} \end{gathered}$

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