Definition of function

Exercise

1.

Find the following rules are single values or multivalued functions．

(a)

$${y^{2} = x, \ x > 0}$$

(b)

$${y^{3} = x^2}$$

2.

Find the domain of the following functions and draw the graph of $f(x)$．

(a)

$${f(x) = \sqrt{4 - x^2}}$$

(b)

$${h(x) = \sqrt{\frac{4x^2 - 3x^3}{6x^2 + 3x}}}$$

3.

Find the composition of $f(x),g(x)$. $(f \circ g)(x)$ and $g(f(x))$.

(a)

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

(b)

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

4.

Find the inverse of the following functions.．

(a)

$${f(x) = \frac{1}{x+2}, \ -2 < x}$$

(b)

$${f(x) = x^2 + 4x - 2}$$