Questions: The inverse of the function (f(x)=frac12 x+10) is shown. [ h(x)=2 x-square ] What is the missing value? 1 5 10 20

Solution Steps

To find the inverse of the function \( f(x) = \frac{1}{2}x + 10 \), we need to solve for \( x \) in terms of \( y \) and then express \( x \) as a function of \( y \). This will give us the inverse function \( h(x) \).

1. Start with the equation \( y = \frac{1}{2}x + 10 \).
2. Solve for \( x \) in terms of \( y \).
3. Replace \( y \) with \( x \) to get the inverse function \( h(x) \).

The original function is given by \[ f(x) = \frac{1}{2}x + 10. \]

To find the inverse, we set \[ y = \frac{1}{2}x + 10. \]

Rearranging the equation to solve for \( x \): \[ y - 10 = \frac{1}{2}x \implies x = 2(y - 10) = 2y - 20. \]

Replacing \( y \) with \( x \) gives us the inverse function: \[ h(x) = 2x - 20. \]

Final Answer