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

Understand the problem: Understand the problem. We need to find the inverse function of f(x) = ((x)/(7))^7, which we will denote as f^(-1)(x). The inverse function will undo the operation of f(x), meaning if f(a) = b, then f^(-1)(b) = a.Write function with y: Write the original function with y instead of f(x). Let y = ((x)/(7))^7. We will solve for x in terms of y to find the inverse function.Swap x and y: Swap x and y. To find the inverse function, we swap x and y in the equation. So we get x = ((y)/(7))^7.Solve for y: Solve for y. To solve for y, we need to take the 7th root of both sides of the equation to get rid of the exponent on the right side. This gives us the 7th root of x equals y/7, or y = 7 * (7th root of x).

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

f^(-1)(x)=root(7)((7x))

f^(-1)(x)=root(7)(((x)/(7)))

f^(-1)(x)=7root(7)(x)

f^(-1)(x)=(root(7)(x))/(7)

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

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. For the function

f(x)=\left(\frac{x}{7}\right)^{7}

, find

f^{-1}(x)

\newline

f^{-1}(x)=\sqrt[7]{(7 x)}

\newline

f^{-1}(x)=\sqrt[7]{\left(\frac{x}{7}\right)}

\newline

f^{-1}(x)=7 \sqrt[7]{x}

\newline

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

Understand the problem: Understand the problem. $\newline$ We need to find the inverse function of $f(x) = \left(\frac{x}{7}\right)^7$ , which we will denote as $f^{-1}(x)$ . The inverse function will undo the operation of $f(x)$ , meaning if $f(a) = b$ , then $f^{-1}(b) = a$ .
Write function with y: Write the original function with y instead of $f(x)$ . $\newline$ Let $y = \left(\frac{x}{7}\right)^7$ . We will solve for $x$ in terms of $y$ to find the inverse function.
Swap $x$ and $y$ : Swap $x$ and $y$ . $\newline$ To find the inverse function, we swap $x$ and $y$ in the equation. So we get $x = \left(\frac{y}{7}\right)^7$ .
Solve for y: Solve for y. $\newline$ To solve for y, we need to take the $7$ th root of both sides of the equation to get rid of the exponent on the right side. This gives us the $7$ th root of $x$ equals $y/7$ , or $y = 7 \times (7$ th root of $x)$ .