WAEC - Further Mathematics (2024 - No. 10)

If f(x) = \(\frac{2 - x}{x}\), x ≠ 0, find the inverse of f.

\(\frac{2}{x - 1}\), x ≠ 1

\(\frac{2}{x+1}\), x ≠ -1

\(\frac{2}{1-x}\), x ≠ 1

\(\frac{x}{2 + x}\), x ≠ -2

f(x) = \(\frac{2 - x}{x}\), x ≠ 0

let the inverse of f \(\frac{2 - 1}{x}\), be y

y = \(\frac{2 - x}{x}\),

xy = 2 - x

xy + x = 2

x(y + 1) = 2

x = \(\frac{2}{y + 1}\) ⇒ \(\frac{2}{x +1}\)

Thus, the inverse of f(x) = \(\frac{2 - x}{x}\), x ≠ 0 = \(\frac{2}{x +1}\) provided x ≠ -1