MHB Domain of Function Involving Roots

[mathdad]

Section 3.1
Question 2dFind the domain of the function.

Let CR = CUBE ROOT

s = CR{3t + 12}

Because it is a cube root, I say the domain is ALL REAL NUMBERS.

 

[mathdad]

Domain of Function...2

Set 3.1
Question 6d

Let CR = cube root

K(x) = CR{2x^2 + x - 6}.

Because it is a cube root, I say the domain is ALL REAL NUMBERS.

 

[mathdad]

Domain of Function...3

Set 3.1
Question 10b

Let FR = fifth root

z = FR{5(x - 4)(5 - x)(x + 1)}

Because the index is an odd number, the domain is ALL REAL NUMBERS.

 

[mathdad]

Domain of Function...4

Set 3.1
Question 10d

Let SR = sixth root

z = SR{5(x - 4)(5 - x)(x + 1)}

Because the index is an even number, I must set the radicand to be > or = 0.

5(x - 4)(5 - x)(x + 1) ≥ 0

Is this correct so far?

 

[kaliprasad]

Re: Domain of Function...1

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.

you can take cube root of -ve nuimbers also so $ - \infty <3t+12 < \infty$ or $ - \infty < t < \infty$

 

[Greg]

Re: Domain of Function...1

What is the cube root of, say, -8? What does the answer to this question tell you about the cube root function?

 

[Greg]

Re: Domain of Function...4

$$x^6=(x^2)^3$$

What can you conclude from the above? In general, what about odd powers? What about even powers?

 

[skeeter]

Re: Domain of Function...2

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?

No.

 

[skeeter]

Re: Domain of Function...3

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?

No.

 

[HallsofIvy]

Re: Domain of Function...3

Consider the distinction between even roots (square roots, fourth roots, etc.) and odd roots (cube root, fourth root, etc.)

 

[Greg]

Re: Domain of Function...1

I've merged the four threads pertaining to the domain of a function into one thread to facilitate a more focused discussion.

 

[mathdad]

Re: Domain of Function...1

What is the cube root of, say, -8? What does the answer to this question tell you about the cube root function?

The cube root of -8 is -2.

- - - Updated - - -

I've merged the four threads pertaining to the domain of a function into one thread to facilitate a more focused discussion.

That's perfectly ok. 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.

 

[mathdad]

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?

 

[MarkFL]

Re: Domain of Function...1

...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.

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

 

[mathdad]

Re: Domain of Function...4

you can take cube root of -ve nuimbers also so $ - \infty <3t+12 < \infty$ or $ - \infty < t < \infty$

Sorry but I do not understand your reply.

 

[mathdad]

Re: Domain of Function...1

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

You are right. In fact, Calculus 1 is considered to be the first math course for people majoring in math in most CUNY colleges. When I took precalculus at Lehman College, the professor made it clear that the material in precalculus courses is taught in 11th or 12th grade in most public high schools.

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?

 

[MarkFL]

Re: Domain of Function...1

...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?

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.

 

[mathdad]

Re: Domain of Function...1

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.

Section 3.1
Question 2d

Find the domain of the function.

Let CR = CUBE ROOT

s = CR{3t + 12}

Because it is a cube root, I say the domain is ALL REAL NUMBERS.

Set 3.1
Question 6d

Let CR = cube root

K(x) = CR{2x^2 + x - 6}.

Because it is a cube root, I say the domain is ALL REAL NUMBERS.

Set 3.1
Question 10b

Let FR = fifth root

z = FR{5(x - 4)(5 - x)(x + 1)}

Because the index is an odd number, the domain is ALL REAL NUMBERS.

Set 3.1
Question 10d

Let SR = sixth root

z = SR{5(x - 4)(5 - x)(x + 1)}

Because the index is an even number, I must set the radicand to be > or = 0.

5(x - 4)(5 - x)(x + 1) ≥ 0

Is this correct so far?