Find the domain of each function using interval notation.
\[
f(x)=\frac{5 x+9}{9 x-2} \quad g(x)=\frac{\sqrt{x+9}}{x-7} \quad h(x)=\frac{x-7}{x^{2}+13 x+36}
\]
(Click here for help with interval notation.)
a. Domain of $f$ :
b. Domain of $g$ :
c. Domain of $h$ :
Answer
Determine the domain of each function using interval notation: \(f(x): (-\infty, \frac{2}{9}) \cup (\frac{2}{9}, \infty)\), \(g(x): [-9, 7) \cup (7, \infty)\), \(h(x): (-\infty, -4) \cup (-4, -9) \cup (-9, \infty)\)
Step 1 ：Find the values of x for which the denominators are not equal to zero: f(x): 9x - 2 ≠ 0, g(x): x - 7 ≠ 0, h(x): x^2 + 13x + 36 ≠ 0
Step 2 ：Determine the domain of each function using interval notation: \(f(x): (-\infty, \frac{2}{9}) \cup (\frac{2}{9}, \infty)\), \(g(x): [-9, 7) \cup (7, \infty)\), \(h(x): (-\infty, -4) \cup (-4, -9) \cup (-9, \infty)\)
