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I am drawing a problem, can someone please help me
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|dw:1356463791314:dw|IT SAYS TO FIND F-1 (X) IN F(X)=^3 SQ X-8 AND SIMPLIFY. cAN ANYONE HELP ME
PLEASE HELP ME WITH THIS PROBLEM.....iM HAVING PROBLEMS\[f-1(x) ........f(x)=^{3}\sqrt{x-8}\]
So we want to find \(f^{-1}(x)\) and we have \(f(x)= \sqrt[3]{x-8}\)?
The solution is to find set \(f(x) = y\) and solve for \(x\) in terms of \(y\).
\[ \Large \begin{array}{lcl} y &=& \sqrt[3]{x-8} \\ y^3 &=& (\sqrt[3]{x-8})^3 \\ y^3 &=& x-8 \\ y^3 +8 &=& x-8+8 \\ y^3 +8 &=& x \\ f^{-1}(y) &=& y^3+8 \\ f^{-1}(x) &=& x^3+8 \end{array} \]
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