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What is the inverse of the function {:[h(x)=(3)/(2)(x-11)?],[h^(-1)(x)=]:}

What is the inverse of the function h(x)=32(x−11) h(x) = \frac{3}{2}(x - 11) ? h−1(x)= h^{-1}(x) =

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Q. What is the inverse of the function h(x)=32(x−11) h(x) = \frac{3}{2}(x - 11) ? h−1(x)= h^{-1}(x) =
  1. Rewriting the function: To find the inverse of the function h(x)h(x), we need to switch the roles of xx and yy and then solve for yy. Let's start by rewriting the function with yy instead of h(x)h(x):\newliney=(32)(x−11)y = \left(\frac{3}{2}\right)(x - 11)
  2. Switching x and y: Now, we switch x and y to find the inverse:\newlinex=(32)(y−11)x = \left(\frac{3}{2}\right)(y - 11)
  3. Solving for y: Next, we solve for y. Start by multiplying both sides by 23\frac{2}{3} to isolate the term with y:\newline(23)x=y−11\left(\frac{2}{3}\right)x = y - 11
  4. Adding 1111: Now, add 1111 to both sides to solve for yy:y=(23)x+11y = \left(\frac{2}{3}\right)x + 11
  5. Inverse function: We have found the expression for yy in terms of xx, which is the inverse function of h(x)h(x). Therefore, the inverse function h−1(x)h^{-1}(x) is:\newlineh−1(x)=(23)x+11h^{-1}(x) = \left(\frac{2}{3}\right)x + 11

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