For the function f(x)=(6-x)/(8-5x), find f^(-1)(x). Answer: f^(-1)(x)=

Replace with y: To find the inverse function, f^(-1)(x), we need to switch the roles of x and y in the original function and then solve for y. Let's start by replacing f(x) with y: y = (6-x)/(8-5x)Switch x and y: Now, switch x and y to find the inverse: x = (6-y)/(8-5y)Eliminate the fraction: Next, we need to solve for y. To do this, we'll multiply both sides of the equation by (8-5y) to eliminate the fraction: x(8-5y) = 6-yDistribute x: Distribute x on the left side of the equation: 8x - 5xy = 6 - yIsolate y terms: Now, we want to get all the terms with y on one side and the constant terms on the other side. Let's add y to both sides and subtract 8x from both sides: -5xy + y = 6 - 8xFactor out y: Factor out y on the left side of the equation: y(-5x + 1) = 6 - 8xSolve for y: Now, divide both sides by (-5x + 1) to solve for y: y = (6 - 8x)/(-5x + 1)Final Inverse Function: We have found the inverse function. Therefore, the inverse function f^(-1)(x) is: f^(-1)(x) = (6 - 8x)/(-5x + 1)

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For the function
f(x)=(6-x)/(8-5x), find
f^(-1)(x).
Answer:
f^(-1)(x)=

For the function $f(x)=\frac{6-x}{8-5 x}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$

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Algebra 1

Write variable expressions for arithmetic sequences

Full solution

Q. For the function

f(x)=\frac{6-x}{8-5 x}

, find

f^{-1}(x)

\newline

Answer:

f^{-1}(x)=

Replace with y: To find the inverse function, $f^{-1}(x)$ , we need to switch the roles of $x$ and $y$ in the original function and then solve for $y$ . Let's start by replacing $f(x)$ with $y$ : $\newline$ $y = \frac{6-x}{8-5x}$
Switch x and y: Now, switch x and y to find the inverse: $x = \frac{6-y}{8-5y}$
Eliminate the fraction: Next, we need to solve for $y$ . To do this, we'll multiply both sides of the equation by $(8-5y)$ to eliminate the fraction: $\newline$ $x(8-5y) = 6-y$
Distribute $x$ : Distribute $x$ on the left side of the equation: $8x - 5xy = 6 - y$
Isolate y terms: Now, we want to get all the terms with y on one side and the constant terms on the other side. Let's add $y$ to both sides and subtract $8x$ from both sides: $\newline$ $-5xy + y = 6 - 8x$
Factor out $y$ : Factor out $y$ on the left side of the equation: $\newline$ $y(-5x + 1) = 6 - 8x$
Solve for y: Now, divide both sides by $(-5x + 1)$ to solve for y: $\newline$ $y = \frac{6 - 8x}{-5x + 1}$
Final Inverse Function: We have found the inverse function. Therefore, the inverse function $f^{-1}(x)$ is: $\newline$ $f^{-1}(x) = \frac{6 - 8x}{-5x + 1}$