Question 24
The functions f and g are defined as follows.
$\mathrm{f}(x) = x^2 + 4x + 2 \quad \text{for } x \le -2$
$\mathrm{g}(x) = -x - 4 \quad \text{for } x \ge -2$
**(ii)** Find an expression for $(\mathrm{gf})^{-1}(x)$.
(In part (a) you found $x^2 + 4x + 2 = (x + 2)^2 - 2$.) (In part (b)(i) you found $\mathrm{f}^{-1}(x) = -\sqrt{x + 2} - 2$.)
$\mathrm{f}(x) = x^2 + 4x + 2 \quad \text{for } x \le -2$
$\mathrm{g}(x) = -x - 4 \quad \text{for } x \ge -2$
**(ii)** Find an expression for $(\mathrm{gf})^{-1}(x)$.
(In part (a) you found $x^2 + 4x + 2 = (x + 2)^2 - 2$.) (In part (b)(i) you found $\mathrm{f}^{-1}(x) = -\sqrt{x + 2} - 2$.)
