Find the inverse function of the function f(x)=(4x)^((9)/(5)) on the domain x >= 0. f^(-1)(x)=(x^((5)/(9)))/(4) f^(-1)(x)=((x)/(4))^((5)/(9)) f^(-1)(x)=(x^((9)/(5)))/(4) f^(-1)(x)=((x)/(4))^((9)/(5))

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: y = (4x)^(9/5)Switch x and y: Now, we switch x and y to find the inverse function: x = (4y)^(9/5)Isolate y: To solve for y, we need to isolate y on one side of the equation. We start by raising both sides of the equation to the power of 5/9 to cancel out the exponent on the right side: (x)^(5/9) = ((4y)^(9/5))^(5/9)Raise to power: When we raise a power to a power, we multiply the exponents. In this case, (9/5) * (5/9) = 1, so we are left with: (x)^(5/9) = 4yDivide by 4: Now, we divide both sides by 4 to solve for y: y = (x^(5/9)) / 4Find inverse function: We have found the inverse function, which we denote as f^(-1)(x): f^(-1)(x) = (x^(5/9)) / 4

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Find the inverse function of the function
f(x)=(4x)^((9)/(5)) on the domain
x >= 0.

f^(-1)(x)=(x^((5)/(9)))/(4)

f^(-1)(x)=((x)/(4))^((5)/(9))

f^(-1)(x)=(x^((9)/(5)))/(4)

f^(-1)(x)=((x)/(4))^((9)/(5))

Find the inverse function of the function $f(x)=(4 x)^{\frac{9}{5}}$ on the domain $x \geq 0$ . $\newline$ $f^{-1}(x)=\frac{x^{\frac{5}{9}}}{4}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{4}\right)^{\frac{5}{9}}$ $\newline$ $f^{-1}(x)=\frac{x^{\frac{9}{5}}}{4}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{4}\right)^{\frac{9}{5}}$

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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{9}{5}}

on the domain

x \geq 0

\newline

f^{-1}(x)=\frac{x^{\frac{5}{9}}}{4}

\newline

f^{-1}(x)=\left(\frac{x}{4}\right)^{\frac{5}{9}}

\newline

f^{-1}(x)=\frac{x^{\frac{9}{5}}}{4}

\newline

f^{-1}(x)=\left(\frac{x}{4}\right)^{\frac{9}{5}}

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 $y$ : $y = (4x)^{\frac{9}{5}}$
Switch x and y: Now, we switch x and y to find the inverse function: $\newline$ $x = (4y)^{\frac{9}{5}}$
Isolate y: To solve for y, we need to isolate y on one side of the equation. We start by raising both sides of the equation to the power of $\frac{5}{9}$ to cancel out the exponent on the right side: $(x)^{\frac{5}{9}} = ((4y)^{\frac{9}{5}})^{\frac{5}{9}}$
Raise to power: When we raise a power to a power, we multiply the exponents. In this case, $(\frac{9}{5}) \times (\frac{5}{9}) = 1$ , so we are left with: $(x)^{\frac{5}{9}} = 4y$
Divide by $4$ : Now, we divide both sides by $4$ to solve for $y$ : $y = \frac{x^{(5/9)}}{4}$
Find inverse function: We have found the inverse function, which we denote as $f^{-1}(x)$ : $\newline$ $f^{-1}(x) = \frac{x^{\frac{5}{9}}}{4}$