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What is the inverse of the function {:[g(x)=-(2)/(3)x-5?],[g^(-1)(x)=]:}

What is the inverse of the function g(x)=−23x−5 g(x) = -\frac{2}{3}x - 5 ? g−1(x)= g^{-1}(x) =

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Q. What is the inverse of the function g(x)=−23x−5 g(x) = -\frac{2}{3}x - 5 ? g−1(x)= g^{-1}(x) =
  1. Replace g(x)g(x) with yy: To find the inverse of the function g(x)=−(23)x−5g(x) = -\left(\frac{2}{3}\right)x - 5, we first replace g(x)g(x) with yy for easier manipulation.\newliney=−(23)x−5y = -\left(\frac{2}{3}\right)x - 5
  2. Swap xx and yy: Next, we swap xx and yy to find the inverse function. This means we replace yy with xx and xx with yy in the equation.\newlinex=−(23)y−5x = -\left(\frac{2}{3}\right)y - 5
  3. Solve for y: Now, we solve for y to get the inverse function. First, we add 55 to both sides of the equation to isolate the term with yy on one side.\newlinex+5=−(23)yx + 5 = -\left(\frac{2}{3}\right)y
  4. Multiply by −32-\frac{3}{2}: Next, we multiply both sides of the equation by −32-\frac{3}{2} to solve for yy. This will cancel out the −(23)-\left(\frac{2}{3}\right) coefficient on the right side.\newline−32×(x+5)=y-\frac{3}{2} \times (x + 5) = y
  5. Simplify the equation: We distribute the −32-\frac{3}{2} across the terms in the parentheses to simplify the equation.\newliney=−32×x−152y = -\frac{3}{2} \times x - \frac{15}{2}

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