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

Rewrite with y: To find the inverse function, we need to switch the roles of x and y in the original function and then solve for y. Let's start by rewriting the function with y: f(x) = (3x)^(7/5) y = (3x)^(7/5) Now we switch x and y: x = (3y)^(7/5)Switch x and y: Next, we need to isolate y. To do this, we raise both sides of the equation to the reciprocal of 7/5, which is 5/7: (x)^(5/7) = ((3y)^(7/5))^(5/7)Isolate y: When we raise a power to a power, we multiply the exponents. In this case, (7/5) * (5/7) = 1, so we are left with: (x)^(5/7) = 3yDivide by 3: Now we divide both sides by 3 to solve for y: y = ((x)^(5/7)) / 3Final Inverse Function: We have found the inverse function. We can write it as: f^(-1)(x) = ((x)^(5/7)) / 3

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

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

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

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

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

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

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Find the inverse function of the function

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

on the domain

x \geq 0

\newline

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

\newline

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

\newline

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

\newline

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

Rewrite with y: To find the inverse function, we need to switch the roles of $x$ and $y$ in the original function and then solve for $y$ . Let's start by rewriting the function with $y$ :
$f(x) = (3x)^{\frac{7}{5}}$
$y = (3x)^{\frac{7}{5}}$
Now we switch $x$ and $y$ :
$x = (3y)^{\frac{7}{5}}$
Switch x and y: Next, we need to isolate $y$ . To do this, we raise both sides of the equation to the reciprocal of $\frac{7}{5}$ , which is $\frac{5}{7}$ : $\newline$ $(x)^{\frac{5}{7}} = ((3y)^{\frac{7}{5}})^{\frac{5}{7}}$
Isolate $y$ : When we raise a power to a power, we multiply the exponents. In this case, $\left(\frac{7}{5}\right) \times \left(\frac{5}{7}\right) = 1$ , so we are left with: $x^{\frac{5}{7}} = 3y$
Divide by $3$ : Now we divide both sides by $3$ to solve for $y$ : $y = \frac{{(x)^{\frac{5}{7}}}}{3}$
Final Inverse Function: We have found the inverse function. We can write it as: $\newline$ $f^{-1}(x) = \frac{(x)^{\frac{5}{7}}}{3}$