Find the inverse of each function. f(x)=(-2-3x)/(2)

Switch Roles and Solve: To find the inverse of the function f(x) = (-2 - 3x) / 2, we need to switch the roles of x and f(x) and then solve for the new x. Let y = f(x), so we have y = (-2 - 3x) / 2. Now we switch x and y to get x = (-2 - 3y) / 2.Multiply and Isolate: Next, we need to solve for y. Start by multiplying both sides of the equation by 2 to get rid of the denominator. 2 * x = -2 - 3yDivide and Solve: Now, we isolate the term containing y by adding 2 to both sides of the equation. 2x + 2 = -3yFinal Inverse Function: To solve for y, we divide both sides of the equation by -3. y = (2x + 2) / -3We have found the inverse function. The inverse function of f(x) = (-2 - 3x) / 2 is f^(-1)(x) = (2x + 2) / -3.

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Q. Find the inverse of each function.

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

Switch Roles and Solve: To find the inverse of the function $f(x) = \frac{-2 - 3x}{2}$ , we need to switch the roles of $x$ and $f(x)$ and then solve for the new $x$ . Let $y = f(x)$ , so we have $y = \frac{-2 - 3x}{2}$ . Now we switch $x$ and $y$ to get $x = \frac{-2 - 3y}{2}$ .
Multiply and Isolate: Next, we need to solve for $y$ . Start by multiplying both sides of the equation by $2$ to get rid of the denominator. $2 \times x = -2 - 3y$
Divide and Solve: Now, we isolate the term containing $y$ by adding $2$ to both sides of the equation. $2x + 2 = -3y$
Final Inverse Function: To solve for $y$ , we divide both sides of the equation by $-3$ . $\newline$ $y = \frac{2x + 2}{-3}$
Final Inverse Function: To solve for $y$ , we divide both sides of the equation by $-3$ . $y = \frac{2x + 2}{-3}$ We have found the inverse function. The inverse function of $f(x) = \frac{-2 - 3x}{2}$ is $f^{-1}(x) = \frac{2x + 2}{-3}$ .