Find the inverse function of the function f(x)=5x^(-(7)/(3)) on the domain x > 0. f^(-1)(x)=(x^(-(3)/(7)))/(5) f^(-1)(x)=(x^(-(7)/(3)))/(5) f^(-1)(x)=((x)/(5))^(-(7)/(3)) f^(-1)(x)=((x)/(5))^(-(3)/(7))

Understand Function & Domain: Understand the function and its domain. The given function is f(x) = 5x^(-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 = 5x^(-7/3). Our goal is to express x in terms of y.Isolate x Term: Isolate the term with the variable x. To isolate x, we first divide both sides of the equation by 5. y/5 = x^(-7/3)Raise to Power: Raise both sides of the equation to the power of -3/7 to cancel the exponent on x. (y/5)^(-3/7) = (x^(-7/3))^(-3/7)Simplify Equation: Simplify the right side of the equation. Since the exponents on the right side are inverse operations, they cancel each other out, leaving us with x. (y/5)^(-3/7) = xWrite Inverse Function: Write the inverse function. The inverse function, denoted by f^(-1)(x), is then given by: f^(-1)(x) = (x/5)^(-3/7)

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Find the inverse function of the function
f(x)=5x^(-(7)/(3)) on the domain
x > 0.

f^(-1)(x)=(x^(-(3)/(7)))/(5)

f^(-1)(x)=(x^(-(7)/(3)))/(5)

f^(-1)(x)=((x)/(5))^(-(7)/(3))

f^(-1)(x)=((x)/(5))^(-(3)/(7))

Find the inverse function of the function $f(x)=5 x^{-\frac{7}{3}}$ on the domain x>0 . $\newline$ $f^{-1}(x)=\frac{x^{-\frac{3}{7}}}{5}$ $\newline$ $f^{-1}(x)=\frac{x^{-\frac{7}{3}}}{5}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{5}\right)^{-\frac{7}{3}}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{5}\right)^{-\frac{3}{7}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Find the inverse function of the function

f(x)=5 x^{-\frac{7}{3}}

on the domain

x>0

\newline

f^{-1}(x)=\frac{x^{-\frac{3}{7}}}{5}

\newline

f^{-1}(x)=\frac{x^{-\frac{7}{3}}}{5}

\newline

f^{-1}(x)=\left(\frac{x}{5}\right)^{-\frac{7}{3}}

\newline

f^{-1}(x)=\left(\frac{x}{5}\right)^{-\frac{3}{7}}

Understand Function & Domain: Understand the function and its domain. $\newline$ The given function is $f(x) = 5x^{(-7/3)}$ , 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 $y = 5x^{(-7/3)}$ . Our goal is to express $x$ in terms of $y$ .
Isolate x Term: Isolate the term with the variable $x$ . To isolate $x$ , we first divide both sides of the equation by $5$ . $\frac{y}{5} = x^{(-\frac{7}{3})}$
Raise to Power: Raise both sides of the equation to the power of $-\frac{3}{7}$ to cancel the exponent on $x$ . $\left(\frac{y}{5}\right)^{-\frac{3}{7}} = \left(x^{-\frac{7}{3}}\right)^{-\frac{3}{7}}$
Simplify Equation: Simplify the right side of the equation. $\newline$ Since the exponents on the right side are inverse operations, they cancel each other out, leaving us with $x$ . $\newline$ $(y/5)^{(-3/7)} = x$
Write Inverse Function: Write the inverse function. $\newline$ The inverse function, denoted by $f^{-1}(x)$ , is then given by: $\newline$ $f^{-1}(x) = \left(\frac{x}{5}\right)^{-\frac{3}{7}}$