Answer:
(a) f⁻¹(x) = 2x - 8
(b) f⁻¹(4) = 0
Explanation:
This is usually not too difficult if you write the equation as y = f(x), then swap x and y and solve for y.
... y = (1/2)x + 4 . . . . y = f(x)
... x = (1/2)y + 4 . . . . variables swapped
... x - 4 = (1/2)y . . . . . subtract 4
... 2(x -4) = y . . . . . . multiply by 2
... y = 2x - 8 . . . . . . simplify
... f⁻¹(x) = 2x -8
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Evaluating this for x=4, we get
... f⁻¹(4) = 2·4 - 8 = 0