Find the domain of the function. f(x) = 3x/x²-9

Question

A. all real numbers x except x -9

B. all real numbers x such that x>-3 and x <3

C. all real numbers x except x = 0

D. all real numbers x except x = ±3

E. all real numbers x such that x <-3 and x >3

Answer 1

the answer is D. All real numbers x except x = ± 3, if you substitute x = 3 or x = - 3 into the denominator

x² -9 you get ( 3)² - 9 = (-3)² - 9 = 0, the function has no value when the denominator is zero and therefore the domain is all real numbers except x = 3, and x =-3. As an exercise try plugging other values of x and you will get values for y. I will leave that up for you to do.

Answer 2

In f(x) = 3x/(x² - 9), you do not want the denominator to be zero.

Any number that would result in a zero in the denominator must be excluded from the domain.

Any number that would give a positive 9 in the denominator, must be excluded from the domain.

In f(x) = 3x/(x² - 9)

The denominator is the difference between two perfect squares and can be factored

(x² - 9) = (x + 3)(x - 3)

And f(x) = 3x/(x+ 3)(x - 3)

D. all real numbers except x = ±3

Try them and remember the denominator cannot be zero

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