SAT Math Multiple Choice Question 919: Answer and Explanation

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Question: 919

3. If, what is the domain of f(x)?

  • A. All real numbers
  • B. All integers except zero
  • C. All positive real numbers
  • D. All real numbers except zero

Correct Answer: C



Difficulty: Medium

Category: Passport to Advanced Math / Functions

Strategic Advice: The domain of a function is the set of x-values for which the function is defined (exists). For basic functions, there are only two rules that can't be broken-the quantity under a square root can't be negative, and the denominator of a fraction can't equal 0.

Getting to the Answer: The square root in the denominator tells you that only numbers greater than or equal to 0 are in the function's domain. However, because the x is in the denominator, it can't be equal to 0. Putting these two restrictions together results in a domain of all real numbers that are strictly greater than 0, or in other words, all positive real numbers, which is (C).

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