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Find the inverse $\newline$ $f(x)=\sqrt[3]{2x-7}$

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Convert complex numbers between rectangular and polar form

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Q. Find the inverse

\newline

f(x)=\sqrt[3]{2x-7}

Replace with $y$ : To find the inverse of the function $f(x) = \sqrt[3]{2x-7}$ , we first replace $f(x)$ with $y$ for convenience. $\newline$ So, we have $y = \sqrt[3]{2x-7}$ .
Swap $x$ and $y$ : Next, we swap $x$ and $y$ to find the inverse function. This gives us $x = \sqrt[3]{2y-7}$ .
Eliminate cube root: Now, we need to solve for $y$ . To do this, we will cube both sides of the equation to eliminate the cube root. $\newline$ So, we have $x^3 = (2y-7)$ .
Isolate $y$ : Next, we isolate $y$ by adding $7$ to both sides of the equation. $\newline$ This gives us $x^3 + 7 = 2y$ .
Divide by $2$ : Finally, we divide both sides of the equation by $2$ to solve for $y$ . This gives us $y = \frac{x^3 + 7}{2}$ .
Write inverse function: We now have the inverse function, which we can write as $f^{-1}(x) = \frac{x^3 + 7}{2}$ .

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