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avatar+1729 

#9 Help.

NotSoSmart  Feb 12, 2018

Best Answer 

 #2
avatar+1720 
+1

#10, why not?

 

According to the original relation, \(f(x)=\sqrt[3]{x-4}\). There are a few steps that need to be done in order to find the inverse. 

 

#1) Convert to y=-notation. I find that it is easier when working with this notation. This is quite a simple step, wouldn't you agree?

 

\(f(x)=\sqrt[3]{x-4}\Rightarrow y=\sqrt[3]{x-4}\)

 

#2) Now, replace all instances of a "y" with an "x," and replace all instances of an "x" with a "y." This is not a difficult step, either, as you might imagine.

 

\(y=\sqrt[3]{x-4}\Rightarrow x=\sqrt[3]{y-4}\)

 

#3) Solve for y. This step can range in difficulty. In this case, it is quite a simple step. 

 

\(x=\sqrt[3]{y-4}\) Cube both sides.
\(x^3=y-4\) Add 4 to both sides to isolate y.
\(y=x^3+4\)  
   

 

#4) Convert back to function notation since the original problem was given in function notation. This is quite simple, too.

 

\(y=x^3+4\Rightarrow f^{-1}(x)=x^3+4\)

 

#5) Correspond your answer with the answer choices given! 

TheXSquaredFactor  Feb 14, 2018
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2+0 Answers

 #1
avatar+1729 
0

Anyone for number 10?

NotSoSmart  Feb 12, 2018
 #2
avatar+1720 
+1
Best Answer

#10, why not?

 

According to the original relation, \(f(x)=\sqrt[3]{x-4}\). There are a few steps that need to be done in order to find the inverse. 

 

#1) Convert to y=-notation. I find that it is easier when working with this notation. This is quite a simple step, wouldn't you agree?

 

\(f(x)=\sqrt[3]{x-4}\Rightarrow y=\sqrt[3]{x-4}\)

 

#2) Now, replace all instances of a "y" with an "x," and replace all instances of an "x" with a "y." This is not a difficult step, either, as you might imagine.

 

\(y=\sqrt[3]{x-4}\Rightarrow x=\sqrt[3]{y-4}\)

 

#3) Solve for y. This step can range in difficulty. In this case, it is quite a simple step. 

 

\(x=\sqrt[3]{y-4}\) Cube both sides.
\(x^3=y-4\) Add 4 to both sides to isolate y.
\(y=x^3+4\)  
   

 

#4) Convert back to function notation since the original problem was given in function notation. This is quite simple, too.

 

\(y=x^3+4\Rightarrow f^{-1}(x)=x^3+4\)

 

#5) Correspond your answer with the answer choices given! 

TheXSquaredFactor  Feb 14, 2018

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