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What is the inverse of the function {:[h(x)=(5)/(2)x+4?],[h^(-1)(x)=]:}

What is the inverse of the function h(x)=52x+4 h(x) = \frac{5}{2}x + 4 ? h−1(x)= h^{-1}(x) =

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Q. What is the inverse of the function h(x)=52x+4 h(x) = \frac{5}{2}x + 4 ? h−1(x)= h^{-1}(x) =
  1. Switching roles and setting up equation: To find the inverse of the function h(x)=52x+4h(x) = \frac{5}{2}x + 4, we need to switch the roles of xx and h(x)h(x) and then solve for the new xx.
    Let y=h(x)y = h(x), so we have y=52x+4y = \frac{5}{2}x + 4.
    Now we switch xx and yy to find the inverse: x=52y+4x = \frac{5}{2}y + 4.
  2. Isolating the term with yy: Next, we need to solve for yy. To do this, we first subtract 44 from both sides of the equation to isolate the term with yy on one side.\newlinex−4=(52)yx - 4 = \left(\frac{5}{2}\right)y
  3. Solving for y: Now, we multiply both sides of the equation by the reciprocal of (52)(\frac{5}{2}), which is (25)(\frac{2}{5}), to solve for y.\newline(25)(x−4)=y(\frac{2}{5})(x - 4) = y
  4. Simplifying the equation: Simplify the equation to get the inverse function.\newlineh−1(x)=25x−25⋅4h^{-1}(x) = \frac{2}{5}x - \frac{2}{5}\cdot4\newlineh−1(x)=25x−85h^{-1}(x) = \frac{2}{5}x - \frac{8}{5}

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