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What is the inverse of f if f(x) = 3 sqrt (x-5) (see image)

What is the inverse of f if f(x) = 3 sqrt (x-5) (see image)-example-1
User Youans
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1 Answer

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The given function is:


f(x)=\sqrt[3]{x-5}

To find the inverse set f(x)=y


y=\sqrt[3]{x-5}

Now, solve for x:

cube both sides of the equation:


\begin{gathered} y^3=(\sqrt[3]{x-5})^3 \\ \text{Simplify} \\ y^3=x-5 \end{gathered}

Add 5 to both sides:


\begin{gathered} y^3+5=x-5+5 \\ y^3+5=x \end{gathered}

Now, switch x and y and reorder terms:


\begin{gathered} x^3+5=y \\ y=x^3+5 \end{gathered}

Replace y by f^-1(x):


f^(-1)(x)=x^3+5

This is the inverse of the function.

User Villar
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