Question

Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-half x minus three-halves?
f Superscript negative 1 Baseline (x) = one-half x minus three-halves
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Answer 1

If f^{-1}(x) = -(1/2)x - 3/2, then to find f(x) swap x and y and solve for y:

x = -(1/2)y - 3/2
x + 3/2 = -(1/2)y
y = -2(x + 3/2) = -2x - 3

So the inverse (original) function is f(x) = -2x - 3.