Questions: Find the inverse of the function f(x) = 1/2 x - 5. f^(-1)(x) = Draw the functions f and f^(-1)

Solution Steps

The given function is \( f(x) = \frac{1}{2}x - 5 \).

Replace \( f(x) \) with \( y \) to make it easier to work with: \[ y = \frac{1}{2}x - 5 \]

To find the inverse, swap \( x \) and \( y \): \[ x = \frac{1}{2}y - 5 \]

Solve the equation for \( y \):

1. Add 5 to both sides: \[ x + 5 = \frac{1}{2}y \]
2. Multiply both sides by 2: \[ 2(x + 5) = y \]
3. Simplify: \[ y = 2x + 10 \]

Replace \( y \) with \( f^{-1}(x) \): \[ f^{-1}(x) = 2x + 10 \]

Final Answer