The inverse of the function f(x)=(x+1)/(x-2) is (1) f^(-1)(x)=(x+1)/(x+2) (3) f^(-1)(x)=(x+1)/(x-2) (2) f^(-1)(x)=(2x+1)/(x-1) (4) f^(-1)(x)=(x-1)/(x+1)

Replace with y: To find the inverse of the function f(x) = (x+1)/(x-2), we need to switch the roles of x and y in the equation and then solve for y. Let's start by replacing f(x) with y: y = (x+1)/(x-2)Interchange x and y: Now, interchange x and y to find the inverse function: x = (y+1)/(y-2)Multiply by (y-2): Next, we need to solve for y. To do this, we'll multiply both sides of the equation by (y-2) to get rid of the fraction: x(y-2) = y+1Distribute x: Distribute x on the left side of the equation: xy - 2x = y + 1Isolate y: To isolate y, we need to get all the terms with y on one side and the constants on the other. Let's move the y term from the right to the left side by subtracting y from both sides: xy - y = 2x + 1Factor out y: Factor out y from the left side of the equation: y(x - 1) = 2x + 1Divide by (x - 1): Now, divide both sides by (x - 1) to solve for y: y = (2x + 1)/(x - 1)Inverse function found: We have found the inverse function, which is: f^(-1)(x) = (2x + 1)/(x - 1)

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The inverse of the function
f(x)=(x+1)/(x-2) is
(1)
f^(-1)(x)=(x+1)/(x+2)
(3)
f^(-1)(x)=(x+1)/(x-2)
(2)
f^(-1)(x)=(2x+1)/(x-1)
(4)
f^(-1)(x)=(x-1)/(x+1)

The inverse of the function $f(x)=\frac{x+1}{x-2}$ is $\newline$ ( $1$ ) $f^{-1}(x)=\frac{x+1}{x+2}$ $\newline$ ( $3$ ) $f^{-1}(x)=\frac{x+1}{x-2}$ $\newline$ ( $2$ ) $f^{-1}(x)=\frac{2 x+1}{x-1}$ $\newline$ ( $4$ ) $f^{-1}(x)=\frac{x-1}{x+1}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The inverse of the function

f(x)=\frac{x+1}{x-2}

\newline

(

1

)

f^{-1}(x)=\frac{x+1}{x+2}

\newline

(

3

)

f^{-1}(x)=\frac{x+1}{x-2}

\newline

(

2

)

f^{-1}(x)=\frac{2 x+1}{x-1}

\newline

(

4

)

f^{-1}(x)=\frac{x-1}{x+1}

Replace with y: To find the inverse of the function $f(x) = \frac{x+1}{x-2}$ , we need to switch the roles of $x$ and $y$ in the equation and then solve for $y$ . Let's start by replacing $f(x)$ with $y$ : $y = \frac{x+1}{x-2}$
Interchange $x$ and $y$ : Now, interchange $x$ and $y$ to find the inverse function: $x = \frac{y+1}{y-2}$
Multiply by $(y-2)$ : Next, we need to solve for $y$ . To do this, we'll multiply both sides of the equation by $(y-2)$ to get rid of the fraction: $\newline$ $x(y-2) = y+1$
Distribute $x$ : Distribute $x$ on the left side of the equation: $xy - 2x = y + 1$
Isolate y: To isolate y, we need to get all the terms with y on one side and the constants on the other. Let's move the y term from the right to the left side by subtracting y from both sides: $xy - y = 2x + 1$
Factor out $y$ : Factor out $y$ from the left side of the equation: $\newline$ $y(x - 1) = 2x + 1$
Divide by $(x - 1)$ : Now, divide both sides by $(x - 1)$ to solve for $y$ : $y = \frac{2x + 1}{x - 1}$
Inverse function found: We have found the inverse function, which is: $f^{-1}(x) = \frac{2x + 1}{x - 1}$