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.
A domain of function involving roots refers to the set of all possible input values for a function that contains a root, or a value that, when raised to a certain power, equals the output of the function. This set of input values is also known as the independent variable.
To find the domain of a function involving roots, you must consider any restrictions on the input values. This includes values that would result in division by zero or taking the root of a negative number. Additionally, you must consider the type of root being used, such as square roots or cube roots, as this can affect the domain.
Yes, the domain of a function involving roots can include negative values. This is because the input values of a function can be negative, and the root operation will still produce a valid result. However, the domain may be limited by other restrictions, as mentioned in the previous answer.
The domain of a function involving roots can affect the shape and range of the graph. For example, if the domain is restricted to positive values only, the graph will only exist in the positive portion of the coordinate plane. Additionally, the domain can affect the number of roots and their placement on the graph.
The domain and range are closely related in a function involving roots. The domain represents the set of input values, while the range represents the set of output values. The domain can determine the range by limiting the possible output values based on the restrictions and operations within the function.