1.1 FUNCTIONS

(a) double-valued function (b) single-valued function

(a) $D(f) = [-2,2]$ (b) $\displaystyle{D(h) = (-\infty,-\frac{1}{2}) \cup (0, \frac{4}{3}]}$

(a) $\displaystyle{(f \circ g)(x) = 2x^2 + 1, (g \circ f)(x) = 4x^2 - 4x + 2}$

(b) $\displaystyle{(f \circ g)(x) = \left\{\begin{array}{cl} x^2 & x < 0\\ 1 + x ... ...x & x \leq 0\\ - x^2 & 0 < x < 1\\ 1 + x^2 & x \geq 1 \end{array} \right.}$

(a) $\displaystyle{y = \frac{1}{x} - 2}$ (b) $\displaystyle{y = -2 + \sqrt{x + 6} (x \geq -6) y = -2 - \sqrt{x + 6} (x \geq -6)}$

(a) even function (b) odd function

(a) a product of even function and even function is even，a product of even and odd functions is odd

(b) even function is symmetric about $y$ -axis．odd function is symmetric about the origin．