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

What is the inverse of the function\newlineg(x)=−2(x−4)?g−1(x)= \begin{array}{l} g(x)=-2(x-4) ? \\ g^{-1}(x)= \end{array}

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Q. What is the inverse of the function\newlineg(x)=−2(x−4)?g−1(x)= \begin{array}{l} g(x)=-2(x-4) ? \\ g^{-1}(x)= \end{array}
  1. Replace g(x)g(x) with yy: To find the inverse of the function g(x)=−2(x−4)g(x) = -2(x - 4), we need to swap the roles of xx and yy and then solve for yy. Let's start by replacing g(x)g(x) with yy:\newliney=−2(x−4)y = -2(x - 4)
  2. Swap x and y: Now, swap x and y to begin finding the inverse function:\newlinex=−2(y−4)x = -2(y - 4)
  3. Solve for y: Next, we solve for y. Start by dividing both sides of the equation by −2-2 to isolate the term with y:\newlinex−2=y−4\frac{x}{-2} = y - 4
  4. Add 44 to both sides: Now, add 44 to both sides of the equation to solve for yy:y=(x−2)+4y = \left(\frac{x}{-2}\right) + 4
  5. Write the inverse function: Finally, we can write the inverse function using the notation g−1(x)g^{-1}(x):\newlineg−1(x)=(x−2)+4g^{-1}(x) = \left(\frac{x}{-2}\right) + 4

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