What is the domain of the real-valued function $f(x) = \sqrt{\frac{x - 2}{5 - x}}$?

D) $(-\infty, 2] \cup (5, \infty)$

What is the domain of the real-valued function $f(x) = \sqrt{16 - x^2} + \frac{1}{x - 2}$?

D) $(-\infty, -4] \cup [4, \infty)$

Math · Functions & Trigonometry · Math · Function Fundamentals

5 Math practice questions on Domain and range. Questions that assess core concepts and understanding.

Layout:

Choose how questions appear in the preview and test.

Preview the questions below, then start to answer and see your results.

1.
What is the domain of the real-valued function $f(x) = \sqrt{\frac{x - 2}{5 - x}}$ ?
- A) $[2, 5)$
- B) $(2, 5]$
- C) $[2, 5]$
- D) $(-\infty, 2] \cup (5, \infty)$
2.
What is the range of the function $f(x) = 2x^2 - 8x + 11$ defined on the closed interval $[1, 5]$ ?
- A) $[3, 21]$
- B) $[5, 21]$
- C) $[3, 11]$
- D) $[2, 21]$
3.
What is the range of the real-valued function $f(x) = \frac{8}{x^2 + 4}$ ?
- A) $[0, 2]$
- B) $(0, 2]$
- C) $(0, 2)$
- D) $[0, \infty)$
4.
What is the domain of the real-valued function $f(x) = \sqrt{16 - x^2} + \frac{1}{x - 2}$ ?
- A) $(-4, 2) \cup (2, 4)$
- B) $[-4, 4]$
- C) $[-4, 2) \cup (2, 4]$
- D) $(-\infty, -4] \cup [4, \infty)$
5.
What is the range of the real-valued function $f(x) = 5 - \sqrt{4 - x}$ ?
- A) $[5, \infty)$
- B) $(-\infty, 4]$
- C) $(-\infty, 5]$
- D) $[4, \infty)$

Answers and step-by-step solutions appear after you finish the test.