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What is the inverse of the function {:[h(x)=(3)/(4)x+12?],[h^(-1)(x)=]:}

What is the inverse of the function h(x)=34x+12 h(x) = \frac{3}{4}x + 12 ? h−1(x)= h^{-1}(x) =

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Q. What is the inverse of the function h(x)=34x+12 h(x) = \frac{3}{4}x + 12 ? h−1(x)= h^{-1}(x) =
  1. Rewriting h(x)h(x) as yy: 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 h(x)h(x) as yy:\newliney=(34)x+12y = \left(\frac{3}{4}\right)x + 12
  2. Switching x and y: Now, we switch x and y to find the inverse:\newlinex=34y+12x = \frac{3}{4}y + 12
  3. Isolating y: Next, we solve for y by isolating it on one side of the equation. First, we subtract 1212 from both sides:\newlinex−12=(34)yx - 12 = \left(\frac{3}{4}\right)y
  4. Solving for y: Now, we multiply both sides by the reciprocal of (34)(\frac{3}{4}), which is (43)(\frac{4}{3}), to solve for y:\newline(43)(x−12)=y(\frac{4}{3})(x - 12) = y
  5. Simplifying the equation: Simplify the equation to get the inverse function:\newliney = 43x−16\frac{4}{3}x - 16\newlineThis is the inverse function, which we denote as h−1(x)h^{-1}(x):\newlineh−1(x)=43x−16h^{-1}(x) = \frac{4}{3}x - 16

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