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
설명
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