Find the inverse function of the function f(x)=4x^(-(7)/(3)) on the domain x > 0. f^(-1)(x)=((x)/(4))^(-(3)/(7)) f^(-1)(x)=(x^(-(3)/(7)))/(4) f^(-1)(x)=((x)/(4))^(-(7)/(3)) f^(-1)(x)=(x^(-(7)/(3)))/(4)

Understand function and domain: Understand the function and its domain. The given function is f(x) = 4x^(-7/3), and it is defined for x > 0. To find the inverse function, we need to solve for x in terms of y, where y = f(x).Replace with y: Replace f(x) with y to prepare for finding the inverse. Let y = 4x^(-7/3). Our goal is to express x in terms of y.Isolate variable x: Isolate the term with the variable x. To isolate x, we first divide both sides of the equation by 4: y/4 = x^(-7/3).Take to power: Take both sides to the power of -3/7 to get rid of the negative exponent. (x^(-7/3))^(-3/7) = (y/4)^(-3/7).Simplify left side: Simplify the left side of the equation using the property of exponents (a^(m))^n = a^(m*n). x = (y/4)^(-3/7).Write inverse function: Write the inverse function. The inverse function, denoted by f^(-1)(x), is then: f^(-1)(x) = (x/4)^(-3/7).

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Find the inverse function of the function
f(x)=4x^(-(7)/(3)) on the domain
x > 0.

f^(-1)(x)=((x)/(4))^(-(3)/(7))

f^(-1)(x)=(x^(-(3)/(7)))/(4)

f^(-1)(x)=((x)/(4))^(-(7)/(3))

f^(-1)(x)=(x^(-(7)/(3)))/(4)

Find the inverse function of the function $f(x)=4 x^{-\frac{7}{3}}$ on the domain x>0 . $\newline$ $f^{-1}(x)=\left(\frac{x}{4}\right)^{-\frac{3}{7}}$ $\newline$ $f^{-1}(x)=\frac{x^{-\frac{3}{7}}}{4}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{4}\right)^{-\frac{7}{3}}$ $\newline$ $f^{-1}(x)=\frac{x^{-\frac{7}{3}}}{4}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Find the inverse function of the function

f(x)=4 x^{-\frac{7}{3}}

on the domain

x>0

\newline

f^{-1}(x)=\left(\frac{x}{4}\right)^{-\frac{3}{7}}

\newline

f^{-1}(x)=\frac{x^{-\frac{3}{7}}}{4}

\newline

f^{-1}(x)=\left(\frac{x}{4}\right)^{-\frac{7}{3}}

\newline

f^{-1}(x)=\frac{x^{-\frac{7}{3}}}{4}

Understand function and domain: Understand the function and its domain. $\newline$ The given function is $f(x) = 4x^{(-7/3)}$ , and it is defined for x > 0. To find the inverse function, we need to solve for $x$ in terms of $y$ , where $y = f(x)$ .
Replace with $y$ : Replace $f(x)$ with $y$ to prepare for finding the inverse. $\newline$ Let $y = 4x^{(-7/3)}$ . Our goal is to express $x$ in terms of $y$ .
Isolate variable x: Isolate the term with the variable x. $\newline$ To isolate $x$ , we first divide both sides of the equation by $4$ : $\newline$ $\frac{y}{4} = x^{(-\frac{7}{3})}.$
Take to power: Take both sides to the power of $-\frac{3}{7}$ to get rid of the negative exponent. $\newline$ $\left(x^{-\frac{7}{3}}\right)^{-\frac{3}{7}} = \left(\frac{y}{4}\right)^{-\frac{3}{7}}$ .
Simplify left side: Simplify the left side of the equation using the property of exponents $(a^{m})^{n} = a^{m*n}$ . $\newline$ $x = (\frac{y}{4})^{(-\frac{3}{7})}$ .
Write inverse function: Write the inverse function. $\newline$ The inverse function, denoted by $f^{-1}(x)$ , is then: $\newline$ $f^{-1}(x) = \left(\frac{x}{4}\right)^{-\frac{3}{7}}$ .