The discussion centers on determining the domain of functions involving roots, specifically cube roots, fifth roots, and sixth roots. It is established that for odd roots, such as cube and fifth roots, the domain is all real numbers. Conversely, for even roots, like sixth roots, the radicand must be non-negative, leading to inequalities such as 5(x - 4)(5 - x)(x + 1) ≥ 0. The participants clarify that cube roots can accept negative values, affirming that the domain remains unrestricted for odd roots.
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RTCNTC said:Section 3.1
Question 2dFind the domain of the function.
Let CR = CUBE ROOT
s = CR{3t + 12}
Do I set 3t + 12 to be > or = 0? I don't recall if this applies to cube roots.
RTCNTC said:Set 3.1
Question 6d
Let CR = cube root
K(x) = CR{2x^2 + x - 6}.
Must I set the radicand to be > or = 0?
RTCNTC said:Set 3.1
Question 10b
Let FR = fifth root
z = FR{5(x - 4)(5 - x)(x + 1)}
Must I set the radicand to be > or = 0?
greg1313 said:What is the cube root of, say, -8? What does the answer to this question tell you about the cube root function?
greg1313 said:I've merged the four threads pertaining to the domain of a function into one thread to facilitate a more focused discussion.
RTCNTC said:...I made a mistake and posted all domain of a function questions in the Pre-University Math forum. Obviously, all my questions come from David Cohen's precalculus textbook.
kaliprasad said:you can take cube root of -ve nuimbers also so $ - \infty <3t+12 < \infty$ or $ - \infty < t < \infty$
MarkFL said:Even though Pre-Calculus is taught in universities, it's really considered a remedial course at that level, and so that's why we classify it as a Pre-University level course. :D
RTCNTC said:...Mark,
I found the following rules online:
f(x) = nthroot{x}
If n is even, x must be > or = 0.
Thus, f(x) is also > or = 0.
If n is odd, x can be any real number.
Thus, f(x) is also any real number.
Can I apply the above rules to my domain questions?
Section 3.1MarkFL said:As long as the radical is not a factor in a denominator (in that case the radicand cannot be zero), then yes that rule can be applied for domain questions. It comes from the fact that an even power of a negative value will be positive, while an odd power of a negative value will be negative.