For the function f(x)=6x^(7)-4, find f^(-1)(x). f^(-1)(x)=(root(7)(x+4))/(6) f^(-1)(x)=root(7)((x+4)/(6)) f^(-1)(x)=root(7)((x)/(6))+4 f^(-1)(x)=(root(7)(x))/(6)+4

Define Original Function: To find the inverse function, f^(-1)(x), we need to switch the roles of x and y in the original function and then solve for y. The original function is f(x) = 6x^7 - 4, which we can write as y = 6x^7 - 4.Replace y with x: Replace y with x to begin finding the inverse function: x = 6y^7 - 4.Isolate y term: Add 4 to both sides of the equation to isolate the term containing y: x + 4 = 6y^7.Divide by 6: Divide both sides of the equation by 6 to further isolate the y term: (x + 4)/6 = y^7.Take 7th root: Take the 7th root of both sides of the equation to solve for y: y = root(7)((x + 4)/6).Express Inverse Function: Replace y with f^(-1)(x) to express the inverse function: f^(-1)(x) = root(7)((x + 4)/6).

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For the function
f(x)=6x^(7)-4, find
f^(-1)(x).

f^(-1)(x)=(root(7)(x+4))/(6)

f^(-1)(x)=root(7)((x+4)/(6))

f^(-1)(x)=root(7)((x)/(6))+4

f^(-1)(x)=(root(7)(x))/(6)+4

For the function $f(x)=6 x^{7}-4$ , find $f^{-1}(x)$ . $\newline$ $f^{-1}(x)=\frac{\sqrt[7]{x+4}}{6}$ $\newline$ $f^{-1}(x)=\sqrt[7]{\frac{x+4}{6}}$ $\newline$ $f^{-1}(x)=\sqrt[7]{\frac{x}{6}}+4$ $\newline$ $f^{-1}(x)=\frac{\sqrt[7]{x}}{6}+4$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. For the function

f(x)=6 x^{7}-4

, find

f^{-1}(x)

\newline

f^{-1}(x)=\frac{\sqrt[7]{x+4}}{6}

\newline

f^{-1}(x)=\sqrt[7]{\frac{x+4}{6}}

\newline

f^{-1}(x)=\sqrt[7]{\frac{x}{6}}+4

\newline

f^{-1}(x)=\frac{\sqrt[7]{x}}{6}+4

Define Original Function: To find the inverse function, $f^{-1}(x)$ , we need to switch the roles of $x$ and $y$ in the original function and then solve for $y$ . The original function is $f(x) = 6x^7 - 4$ , which we can write as $y = 6x^7 - 4$ .
Replace $y$ with $x$ : Replace $y$ with $x$ to begin finding the inverse function: $x = 6y^7 - 4$ .
Isolate y term: Add $4$ to both sides of the equation to isolate the term containing $y$ : $x + 4 = 6y^7$ .
Divide by $6$ : Divide both sides of the equation by $6$ to further isolate the y term: $(x + 4)/6 = y^7$ .
Take $7$ th root: Take the $7$ th root of both sides of the equation to solve for $y$ : $y = \sqrt[7]{\frac{x + 4}{6}}$ .
Express Inverse Function: Replace $y$ with $f^{-1}(x)$ to express the inverse function: $f^{-1}(x) = \sqrt[7]{\frac{x + 4}{6}}$ .