What is the inverse of the function {:[g(x)=-3(x+6)?],[g^(-1)(x)=]:}

Replace g(x) with y: To find the inverse of the function g(x) = -3(x + 6), we need to switch the roles of x and y and then solve for y. Let's start by replacing g(x) with y: y = -3(x + 6)Switch x and y: Now we switch x and y to find the inverse: x = -3(y + 6)Solve for y: Next, we solve for y by isolating it on one side of the equation. Start by dividing both sides by -3 to undo the multiplication: x / -3 = y + 6Isolate y: Now, subtract 6 from both sides to isolate y: (x / -3) - 6 = yWrite the inverse function: Finally, we write the inverse function by replacing y with g^(-1)(x): g^(-1)(x) = (x / -3) - 6

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Algebra 2

Identify inverse functions

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Q. What is the inverse of the function

\newline

\begin{array}{l} g(x)=-3(x+6) ? \\ g^{-1}(x)= \end{array}

Replace $g(x)$ with $y$ : To find the inverse of the function $g(x) = -3(x + 6)$ , we need to switch the roles of $x$ and $y$ and then solve for $y$ . Let's start by replacing $g(x)$ with $y$ : $\newline$ $y = -3(x + 6)$
Switch x and y: Now we switch x and y to find the inverse: $\newline$ $x = -3(y + 6)$
Solve for y: Next, we solve for y by isolating it on one side of the equation. Start by dividing both sides by $-3$ to undo the multiplication: $\newline$ $\frac{x}{-3} = y + 6$
Isolate y: Now, subtract $6$ from both sides to isolate y: $\frac{x}{-3} - 6 = y$
Write the inverse function: Finally, we write the inverse function by replacing $y$ with $g^{-1}(x)$ : $g^{-1}(x) = \left(\frac{x}{-3}\right) - 6$