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

Replace with y: To find the inverse function, we start by replacing f(x) with y for easier manipulation. y = (x^(1/3))/7Swap x and y: Next, we swap x and y to begin solving for the inverse function. x = (y^(1/3))/7Isolate y: Now, we solve for y by isolating it on one side of the equation. We start by multiplying both sides by 7 to get rid of the denominator. 7x = y^(1/3)Eliminate cube root: To eliminate the cube root, we raise both sides of the equation to the power of 3. (7x)^3 = (y^(1/3))^3Simplify equation: Raising both sides to the power of 3, we simplify the equation. 343x^3 = yReplace with f^(-1)(x): Finally, we replace y with f^(-1)(x) to denote the inverse function. f^(-1)(x) = 343x^3

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

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

f^(-1)(x)=(7x)^(3)

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

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

For the function $f(x)=\frac{x^{\frac{1}{3}}}{7}$ , find $f^{-1}(x)$ . $\newline$ $f^{-1}(x)=7 x^{\frac{1}{3}}$ $\newline$ $f^{-1}(x)=(7 x)^{3}$ $\newline$ $f^{-1}(x)=(7 x)^{\frac{1}{3}}$ $\newline$ $f^{-1}(x)=\frac{x^{3}}{7}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. For the function

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

, find

f^{-1}(x)

\newline

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

\newline

f^{-1}(x)=(7 x)^{3}

\newline

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

\newline

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

Replace with $y$ : To find the inverse function, we start by replacing $f(x)$ with $y$ for easier manipulation. $\newline$ $y = \frac{x^{\frac{1}{3}}}{7}$
Swap x and y: Next, we swap x and y to begin solving for the inverse function. $\newline$ $x = \frac{y^{\frac{1}{3}}}{7}$
Isolate y: Now, we solve for y by isolating it on one side of the equation. We start by multiplying both sides by $7$ to get rid of the denominator. $\newline$ $7x = y^{(1/3)}$
Eliminate cube root: To eliminate the cube root, we raise both sides of the equation to the power of $3$ . $(7x)^3 = (y^{1/3})^3$
Simplify equation: Raising both sides to the power of $3$ , we simplify the equation. $343x^3 = y$
Replace with $f^{-1}(x)$ : Finally, we replace $y$ with $f^{-1}(x)$ to denote the inverse function. $\newline$ $f^{-1}(x) = 343x^3$