For the function f(x)=(x^(3)-8)/(5), find f^(-1)(x). f^(-1)(x)=5root(3)(x)+8 f^(-1)(x)=root(3)(5x+8) f^(-1)(x)=root(3)(5(x+8)) f^(-1)(x)=5root(3)(x+8)

Eliminate denominator by multiplication: Multiply both sides by 5 to eliminate the denominator: 5x = y^3 - 8Isolate cubic term by addition: Add 8 to both sides to isolate the cubic term: 5x + 8 = y^3Solve for y by taking cube root: Take the cube root of both sides to solve for y: y = root(3)(5x + 8)Write inverse function: Now that we have solved for y, we can write the inverse function as: f^(-1)(x) = root(3)(5x + 8)

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For the function
f(x)=(x^(3)-8)/(5), find
f^(-1)(x).

f^(-1)(x)=5root(3)(x)+8

f^(-1)(x)=root(3)(5x+8)

f^(-1)(x)=root(3)(5(x+8))

f^(-1)(x)=5root(3)(x+8)

For the function $f(x)=\frac{x^{3}-8}{5}$ , find $f^{-1}(x)$ . $\newline$ $f^{-1}(x)=5 \sqrt[3]{x}+8$ $\newline$ $f^{-1}(x)=\sqrt[3]{5 x+8}$ $\newline$ $f^{-1}(x)=\sqrt[3]{5(x+8)}$ $\newline$ $f^{-1}(x)=5 \sqrt[3]{x+8}$

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Calculus

Find derivatives of using multiple formulae

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Q. For the function

f(x)=\frac{x^{3}-8}{5}

, find

f^{-1}(x)

\newline

f^{-1}(x)=5 \sqrt[3]{x}+8

\newline

f^{-1}(x)=\sqrt[3]{5 x+8}

\newline

f^{-1}(x)=\sqrt[3]{5(x+8)}

\newline

f^{-1}(x)=5 \sqrt[3]{x+8}

Eliminate denominator by multiplication: Multiply both sides by $5$ to eliminate the denominator: $\newline$ $5x = y^3 - 8$
Isolate cubic term by addition: Add $8$ to both sides to isolate the cubic term: $\newline$ $5x + 8 = y^3$
Solve for $y$ by taking cube root: Take the cube root of both sides to solve for $y$ : $\newline$ $y = \sqrt[3]{5x + 8}$
Write inverse function: Now that we have solved for $y$ , we can write the inverse function as: $\newline$ $f^{-1}(x) = \sqrt[3]{5x + 8}$