What is the inverse of the function {:[g(x)=-2(x-4)?],[g^(-1)(x)=]:}

Replace g(x) with y: To find the inverse of the function g(x) = -2(x - 4), we need to swap the roles of x and y and then solve for y. Let's start by replacing g(x) with y: y = -2(x - 4)Swap x and y: Now, swap x and y to begin finding the inverse function: x = -2(y - 4)Solve for y: Next, we solve for y. Start by dividing both sides of the equation by -2 to isolate the term with y: x / -2 = y - 4Add 4 to both sides: Now, add 4 to both sides of the equation to solve for y: y = (x / -2) + 4Write the inverse function: Finally, we can write the inverse function using the notation g^(-1)(x): g^(-1)(x) = (x / -2) + 4

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Algebra 2

Identify inverse functions

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Q. What is the inverse of the function

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\begin{array}{l} g(x)=-2(x-4) ? \\ g^{-1}(x)= \end{array}

Replace $g(x)$ with $y$ : To find the inverse of the function $g(x) = -2(x - 4)$ , we need to swap the roles of $x$ and $y$ and then solve for $y$ . Let's start by replacing $g(x)$ with $y$ : $\newline$ $y = -2(x - 4)$
Swap x and y: Now, swap x and y to begin finding the inverse function: $\newline$ $x = -2(y - 4)$
Solve for y: Next, we solve for y. Start by dividing both sides of the equation by $-2$ to isolate the term with y: $\newline$ $\frac{x}{-2} = y - 4$
Add $4$ to both sides: Now, add $4$ to both sides of the equation to solve for $y$ : $y = \left(\frac{x}{-2}\right) + 4$
Write the inverse function: Finally, we can write the inverse function using the notation $g^{-1}(x)$ : $\newline$ $g^{-1}(x) = \left(\frac{x}{-2}\right) + 4$