Let

$f (a) = b$ , $b \not= 0$

$f (c) = d$ , $d \not= 0$

$g$ be the inverse of $f$

$h$ is the reciprocal of $f$

Are the following statements true or false?

? True False  1. $f (a) \cdot h(a) = 1$

? True False  2. $\frac {f(c)}{h(c)} = d^2$

? True False  3. The domain of $g$ $=$ the range of $f$.

? True False  4. $g (d) = c$

? True False  5. $f ( \frac{a}{c} ) = \frac{b}{d}$

? True False  6. $g (a) = b$