f(x) = 2−xx\frac{2 - x}{x}x2−x, x ≠ 0
let the inverse of f 2−1x\frac{2 - 1}{x}x2−1, be y
y = 2−xx\frac{2 - x}{x}x2−x,
xy = 2 - x
xy + x = 2
x(y + 1) = 2
x = 2y+1\frac{2}{y + 1}y+12 ⇒ 2x+1\frac{2}{x + 1}x+12
Thus, the inverse of f(x) = 2−xx\frac{2 - x}{x}x2−x, x ≠ 0 = 2x+1\frac{2}{x + 1}x+12 provided x ≠ -1
