For the function f(x)=(3x-5)/(2x), find f^(-1)(x). Answer: f^(-1)(x)=

Prepare for finding inverse: Set f(x) equal to y to prepare for finding the inverse function. y = (3x - 5) / (2x)Swap x and y: Swap x and y to find the inverse function. This means we replace y with x and x with y in the equation. x = (3y - 5) / (2y)Clear fraction and solve: Solve for y. To do this, we need to clear the fraction by multiplying both sides of the equation by 2y. 2xy = 3y - 5Get terms on one side: Get all terms containing y on one side of the equation and the constant term on the other side. 2xy - 3y = -5Factor out y: Factor out y from the left side of the equation. y(2x - 3) = -5Divide to solve for y: Divide both sides of the equation by (2x - 3) to solve for y. y = -5 / (2x - 3)Replace with inverse function: Replace y with f^(-1)(x) to denote the inverse function. f^(-1)(x) = -5 / (2x - 3)

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For the function
f(x)=(3x-5)/(2x), find
f^(-1)(x).
Answer:
f^(-1)(x)=

For the function $f(x)=\frac{3 x-5}{2 x}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$

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Algebra 2

Write a formula for an arithmetic sequence

Full solution

Q. For the function

f(x)=\frac{3 x-5}{2 x}

, find

f^{-1}(x)

\newline

Answer:

f^{-1}(x)=

Prepare for finding inverse: Set $f(x)$ equal to $y$ to prepare for finding the inverse function. $\newline$ $y = \frac{3x - 5}{2x}$
Swap $x$ and $y$ : Swap $x$ and $y$ to find the inverse function. This means we replace $y$ with $x$ and $x$ with $y$ in the equation. $\newline$ $x = \frac{3y - 5}{2y}$
Clear fraction and solve: Solve for $y$ . To do this, we need to clear the fraction by multiplying both sides of the equation by $2y$ . $2xy = 3y - 5$
Get terms on one side: Get all terms containing $y$ on one side of the equation and the constant term on the other side. $2xy - 3y = -5$
Factor out $y$ : Factor out $y$ from the left side of the equation. $y(2x - 3) = -5$
Divide to solve for y: Divide both sides of the equation by $(2x - 3)$ to solve for y. $\newline$ $y = \frac{-5}{(2x - 3)}$
Replace with inverse function: Replace $y$ with $f^{-1}(x)$ to denote the inverse function. $f^{-1}(x) = \frac{-5}{2x - 3}$