For the function f(x)=7root(3)(x)-10, find f^(-1)(x). f^(-1)(x)=((x+10)^(3))/(7) f^(-1)(x)=((x+10)/(7))^(3) f^(-1)(x)=((x)/(7)+10)^(3) f^(-1)(x)=(x^(3)+10)/(7)

Write function as y: To find the inverse function, we first write the function as y = 7root(3)(x) - 10.Swap x and y: Next, we swap x and y to solve for the inverse function: x = 7root(3)(y) - 10.Isolate cube root term: Now, we isolate the cube root term by adding 10 to both sides: x + 10 = 7root(3)(y).Cube both sides: To remove the cube root, we cube both sides of the equation: (x + 10)^3 = (7root(3)(y))^3.Divide by 7^3: Cubing the right side gives us (x + 10)^3 = 7^3 * y because (root(3)(y))^3 = y.Simplify the equation: Now we divide both sides by 7^3 to solve for y: y = (x + 10)^3 / 7^3.Since 7^3 is 343, we simplify the equation to get the inverse function: f^(-1)(x) = (x + 10)^3 / 343.

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For the function
f(x)=7root(3)(x)-10, find
f^(-1)(x).

f^(-1)(x)=((x+10)^(3))/(7)

f^(-1)(x)=((x+10)/(7))^(3)

f^(-1)(x)=((x)/(7)+10)^(3)

f^(-1)(x)=(x^(3)+10)/(7)

For the function $f(x)=7 \sqrt[3]{x}-10$ , find $f^{-1}(x)$ . $\newline$ $f^{-1}(x)=\frac{(x+10)^{3}}{7}$ $\newline$ $f^{-1}(x)=\left(\frac{x+10}{7}\right)^{3}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{7}+10\right)^{3}$ $\newline$ $f^{-1}(x)=\frac{x^{3}+10}{7}$

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Calculus

Find derivatives of using multiple formulae

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Q. For the function

f(x)=7 \sqrt[3]{x}-10

, find

f^{-1}(x)

\newline

f^{-1}(x)=\frac{(x+10)^{3}}{7}

\newline

f^{-1}(x)=\left(\frac{x+10}{7}\right)^{3}

\newline

f^{-1}(x)=\left(\frac{x}{7}+10\right)^{3}

\newline

f^{-1}(x)=\frac{x^{3}+10}{7}

Write function as $y$ : To find the inverse function, we first write the function as $y = 7\sqrt[3]{x} - 10$ .
Swap x and y: Next, we swap x and y to solve for the inverse function: $x = 7\sqrt[3]{y} - 10$ .
Isolate cube root term: Now, we isolate the cube root term by adding $10$ to both sides: $x + 10 = 7\sqrt[3]{y}$ .
Cube both sides: To remove the cube root, we cube both sides of the equation: $(x + 10)^3 = (7\sqrt[3]{y})^3$ .
Divide by $7^3$ : Cubing the right side gives us $(x + 10)^3 = 7^3 \times y$ because $(\sqrt[3]{y})^3 = y$ .
Simplify the equation: Now we divide both sides by $7^3$ to solve for $y$ : $y = \frac{(x + 10)^3}{7^3}$ .
Simplify the equation: Now we divide both sides by $7^3$ to solve for $y$ : $y = \frac{(x + 10)^3}{7^3}$ .Since $7^3$ is $343$ , we simplify the equation to get the inverse function: $f^{-1}(x) = \frac{(x + 10)^3}{343}$ .