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Math  /  Algebra

QuestionQuestion For the function f(x)=9(x+9)13f(x)=9(x+9)^{\frac{1}{3}}, find f−1(x)f^{-1}(x).
Answer f−1(x)=(x9)3−9f^{-1}(x)=\left(\frac{x}{9}\right)^{3}-9 f−1(x)=(x9−9)3f^{-1}(x)=\left(\frac{x}{9}-9\right)^{3} f−1(x)=x3−99f^{-1}(x)=\frac{x^{3}-9}{9} f−1(x)=(x−9)39f^{-1}(x)=\frac{(x-9)^{3}}{9}

Studdy Solution
Verify and simplify the expression if necessary. The expression is already simplified.
The inverse function is:
f−1(x)=(x9)3−9 f^{-1}(x) = \left(\frac{x}{9}\right)^3 - 9

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