1.1 FUNCTIONS

1.

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

2.

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

3.

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

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

4.

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

5.

(a) even function (b) odd function

6.

(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．