Find Domain of Functions

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 2, Section 2.1

Find the domain of each function.

51. g(x) = x/(x^2 - 16)

Let me see.

For 51, set denominator to 0 and solve for x yields the domain. Yes?

58. p(x) = sqrt{2/(x - 1)}

For 58, house top and bottom into individual square roots.

So, sqrt{2/(x - 1)} becomes
(sqrt{2})/(sqrt{x - 1)}. I now set denominator to be greater than or equal to 0. This will yield the domain of the function. Yes?

61. p(t) = sqrt{t - 4)/(3t - 21)

For 61, we ignore the square root part and set the denominator to 0 and solve for t. This will yield the domain of the function. Yes?

[Eigenvalue]

51. The values 4 and -4 must be excluded from the domain; setting the denominator equal to 0 will result in the values excluded from the domain.

58. Correct

61.The whole fraction needs to be set equal to [tex]\ge[/tex] 0

[nycmath]

Yes, for 51, the domain is all real numbers except for -4 and 4. Plugging -4 or 4 for x yields division by zero which DNE.

Thank for letting me that the whole fraction must be set to be greater than or equal to 0 for 61.