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Exercises 8.5 Practice Problems

1.

Write each of the following in interval notation (Note: you may find it helpful to draw a number line):
  1. \(\displaystyle x \ge -5\)
  2. \(x \le -3\) or \(x \gt 6\)
  3. \(\displaystyle x \neq 88\)
  4. \(x \ge -2\) and \(x \lt 6\)
  5. Everything except \(\pm 6\)
  6. \(\displaystyle x \lt 18\)
  7. Everything except \(0\)
  8. \(x \lt -5\) or \(x \gt -5\)
Answer.
  1. \(\displaystyle [-5, \infty)\)
  2. \(\displaystyle (-\infty,-3]\cup(6,\infty)\)
  3. \(\displaystyle (-\infty,88)\cup(88,\infty)\)
  4. \(\displaystyle [-2, 6)\)
  5. \(\displaystyle (-\infty,-6)\cup(-6,6)\cup(6,\infty)\)
  6. \(\displaystyle (-\infty,18)\)
  7. \(\displaystyle (-\infty,0)\cup(0,\infty)\)
  8. \(\displaystyle (-\infty, -5)\cup(-5, \infty)\)

27.

Find the domain of \(f(x)=\frac{x-3}{12x+18}\text{.}\)
Answer.
\((-\infty, -\frac{3}{2})\cup(-\frac{3}{2}, \infty)\)