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

What is the inverse of the function $g(x) = -3(x+6)$ ? $g^{-1}(x) = \square$

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Find the vertex of the transformed function

Full solution

Q. What is the inverse of the function

g(x) = -3(x+6)

?

g^{-1}(x) = \square

Replace with $y$ : To find the inverse of the function $g(x) = -3(x + 6)$ , we first replace $g(x)$ with $y$ for simplicity. $\newline$ $y = -3(x + 6)$
Swap $x$ and $y$ : Next, we swap $x$ and $y$ to find the inverse function. This means we replace $y$ with $x$ and $x$ with $y$ in the equation. $\newline$ $x = -3(y + 6)$
Isolate y: Now, we solve for y to get the inverse function. First, we divide both sides by $-3$ to isolate the term with y. $\newline$ $\frac{x}{-3} = y + 6$
Subtract $6$ : Next, we subtract $6$ from both sides to solve for $y$ . $\newline$ $\left(\frac{x}{-3}\right) - 6 = y$
Write inverse function: We have found the inverse function. We can now write it as $g^{-1}(x)$ . $\newline$ $g^{-1}(x) = \frac{x}{-3} - 6$

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