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

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Full solution

Q. What is the inverse of the function\newlineg(x)=−3(x+6)?g−1(x)= \begin{array}{l} g(x)=-3(x+6) ? \\ g^{-1}(x)= \end{array}
  1. Replace g(x)g(x) with yy: To find the inverse of the function g(x)=−3(x+6)g(x) = -3(x + 6), we need to switch the roles of xx and yy and then solve for yy. Let's start by replacing g(x)g(x) with yy:\newliney=−3(x+6)y = -3(x + 6)
  2. Switch x and y: Now we switch x and y to find the inverse:\newlinex=−3(y+6)x = -3(y + 6)
  3. Solve for y: Next, we solve for y by isolating it on one side of the equation. Start by dividing both sides by −3-3 to undo the multiplication:\newlinex−3=y+6\frac{x}{-3} = y + 6
  4. Isolate y: Now, subtract 66 from both sides to isolate y: x−3−6=y\frac{x}{-3} - 6 = y
  5. Write the inverse function: Finally, we write the inverse function by replacing yy with g−1(x)g^{-1}(x):g−1(x)=(x−3)−6g^{-1}(x) = \left(\frac{x}{-3}\right) - 6

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