What is the inverse of the function {:[f(x)=-(1)/(2)(x+3)?],[f^(-1)(x)=◻]:}

Switch Roles and Solve: To find the inverse of the function f(x) = -(1/2)(x + 3), 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 = -(1/2)(x + 3). Now, replace y with x to get x = -(1/2)(y + 3).Replace y with x: Next, we need to solve for y. Start by multiplying both sides of the equation by -2 to get rid of the fraction. -2x = y + 3Multiply by -2: Now, subtract 3 from both sides to isolate y. -2x - 3 = yIsolate y: Finally, we write the inverse function by replacing y with f^(-1)(x). f^(-1)(x) = -2x - 3

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Identify inverse functions

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Q. What is the inverse of the function

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\begin{array}{l} f(x)=-\frac{1}{2}(x+3) ? \\ f^{-1}(x)=\square \end{array}

Switch Roles and Solve: To find the inverse of the function $f(x) = -\frac{1}{2}(x + 3)$ , 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 $y = -\frac{1}{2}(x + 3)$ . Now, replace $y$ with $x$ to get $x = -\frac{1}{2}(y + 3)$ .
Replace $y$ with $x$ : Next, we need to solve for $y$ . Start by multiplying both sides of the equation by $-2$ to get rid of the fraction. $\newline$ $-2x = y + 3$
Multiply by $-2$ : Now, subtract $3$ from both sides to isolate $y$ . $-2x - 3 = y$
Isolate y: Finally, we write the inverse function by replacing $y$ with $f^{-1}(x)$ . $f^{-1}(x) = -2x - 3$