Function $f$ is defined by $f : x \mapsto x^{2} + 2x + 3,\ x \le -1$. Show that $f^{-1}$ exists. Hen

Question

Function $f$ is defined by $f : x \mapsto x^{2} + 2x + 3,\ x \le -1$. Show that $f^{-1}$ exists. Hence, find $f^{-1}$, stating its domain and range.

Accepted Answer

f^{-1}(x) = -1 - √(x-2); D = [2, ∞); R = (-∞, -1]

Worked Example 1