Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Find Domain of Functions...1

Find domain for each function.

1. G(x) = (x + 4)/(x^3 - 4x)

2. f(x) = x/sqrt{x - 6}

Question 1

Set denominator to 0 and solve for x.

x^3 - 4x = 0

x(x^2 - 4) = 0

x = 0

x^2 - 4  = 0

x^2 = 4

Taking the square root on each side I get
x = - 2 and x = 2.

Domain = ALL REAL NUMBERS except x cannot be -2, 0, and 2.

You say?

Question 2

Set radicand to be greater than or equal to zero.

x - 6 >= 0

x >= 6 + 0

x >= 6

Domain: x >= 6

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Find Domain of Functions...1

Yes, both good.

In view of what I said in an earlier post I think the responsibility for deciding the domain rests with the questioner.  So I would word this " Assuming the domain is as much of the reals as possible  determine what values of x must be excluded."

This also covers the possibility that x could otherwise be a complex number.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Find Domain of Functions...1

Yes, both good.

In view of what I said in an earlier post I think the responsibility for deciding the domain rests with the questioner.  So I would word this " Assuming the domain is as much of the reals as possible  determine what values of x must be excluded."

This also covers the possibility that x could otherwise be a complex number.

Bob

I agree but math textbooks writing is not always clear and to the point. I find math textbooks to be confusing because not all math teachers have the gift of writing clearly and precisely.