Hey guys having some trouble with these ones still.
Find the domain of $\displaystyle f(x) = -12 / (-9 + x^2)$
Find the range of $\displaystyle f(w) = 3 / (\sqrt{w} - 8)$
Thanks
1.
x can take any number except -3 and 3 since x = -3 and x=3 would make the denominator equal to zero $\displaystyle (-9+9=0)$ and the division by zero is not allowed in mathematics. Hence the domain in interval notation is given by
$\displaystyle (-\infty, -3) \cup (-3,3) \cup (3, \infty)$
Note that neither -3 nor 3 are included in the domain..
to find the range, you have:
$\displaystyle y= f(w) = \frac{3}{(\sqrt{w} - 8)}$
so, $\displaystyle (\sqrt{w} - 8) = \frac{3}{y}$
so, $\displaystyle \sqrt{w} = {\frac{3}{y}}+8 $
thus, $\displaystyle w = ({{\frac{3}{y}}+8})^2 $
y can take any number except 0 since y = 0 would make the denominator equal to zero and the division by zero is not allowed in mathematics. Hence the range in interval notation is given by:
$\displaystyle (-\infty,0) \cup (0,\infty)$