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Mathematics 13 Online
OpenStudy (anonymous):

Find each of the following.

OpenStudy (anonymous):

(fg)(x) = (gf)(x) =

myininaya (myininaya):

so is that suppose to be f times g or f composed of g

OpenStudy (anonymous):

f circle g

OpenStudy (anonymous):

so f(g(x))

OpenStudy (anonymous):

right?

myininaya (myininaya):

\[f(x)=x^3-9\] \[g(x)=\sqrt[3]{x+9}\] \[f \circ g =f(g(x))=f(\sqrt[3]{x+9})=(\sqrt[3]{x+9})^3-9=(x+9)-9=x+9-9=x\]

myininaya (myininaya):

\[g \circ f=g(f(x))=g(x^3-9)=\sqrt[3]{(x^3-9)+9}=\sqrt[3]{x^3}=x\]

myininaya (myininaya):

since both of these =x you can write f and g are inverses of each other

OpenStudy (anonymous):

ok i posted 2 other ones that are similar but different, could u help with those too? i have them on my profile if you dont wanna scroll down through everything here...

OpenStudy (anonymous):

yes?

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