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§A.2 Properties of Continuous Functions 161
˝
Since f ´1 is continuous on f ((a, b)), x Ñ x0 as y Ñ y0; thus
lim f ´1(y) ´ f ´1(y0) = lim x ´ x0 1
=
yÑy0 y ´ y0 xÑx0 f (x) ´ f (x0) f 1(x0)
which implies that f ´1 is differentiable at y0.
