To find the inverse of a function, we need to switch the input and output variables. In other words, we need to solve the equation for x instead of y.
f(x) = ½(x) + 2
Let y = f(x)
y = ½(x) + 2
Subtract 2 from both sides
y – 2 = ½(x)
Multiply both sides by 2
2(y – 2) = x
x = 2y – 4
Therefore, the inverse function of f(x) = ½(x) + 2 is f⁻¹(x) = 2x – 4.
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