18Inverse function value

$\displaystyle f(x) = \dfrac{3x - 1}{x + 2}$. Find $\displaystyle f^{-1}(2)$.

f⁻¹(2) = 5. Since f⁻¹(2) means the x with f(x) = 2, set (3x−1)/(x+2) = 2, clear the fraction to get 3x−1 = 2x+4, then solve to get x = 5. Check: (3·5−1)/(5+2) = 14/7 = 2.