Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Find Domain of Functions...2

Find domain for each function.

1. q(x) = sqrt{- x - 2}

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

Question 1

Set radicand to be greater than or equal to 0.

-x - 2 >= 0

-x >= 2

Divide both sides by -1. Reverse the inequality sign.

-x >= 2

-x/-1 <= 2/-1

x <= -2

Domain: x <= -2

Question 2

p(x) sqrt{(2/(x - 1)}

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

x - 1 >= 0

x >= 1

Domain: x >= 1

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Find Domain of Functions...2

x-1 cannot be equal to 0.

Bob

---

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...2

x-1 cannot be equal to 0.

Bob

I must set the radicand to be > 0.

2/(x - 1) > 0

x - 1 = 0

x = 1

Domain: ALL positive REAL NUMBERS except for 1.

Domain: (1, infinity].

Yes?

Last edited by nycguitarguy (2024-03-09 19:53:12)

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 166

Re: Find Domain of Functions...2

or ]1, ∞]

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Find Domain of Functions...2

or ]1, ∞]

We don't include a bracket in terms of negative or positive infinity.

You meant to say [1, ∞) as another way to express domain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Find Domain of Functions...2

The convention is square brackets if an end point is included and a round bracket if it's not.

As you cannot reach infinity and it doesn't obey the usual rules for numbers it is not regarded as a number.

So 1 isn't included or you have division by zero; infinity isn't included thus (1, ∞)

Bob

---

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

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 166

Re: Find Domain of Functions...2

I agree with you both.
For instance, at my French school (about 58 years ago) we used to write:
[1, 4] which means that the domain is from 1 to 4 with 1 and 4 included.
]1, 4[ which means that the domain is from1 to 4 but 1 and 4 are not included.
]1, ∞] which means that the domain is from 1 to ∞ but 1 ia not included. Infinity was included always since any big number that one may imagine of is included

I learnt from you that the above examples are now written as:
[1, 4]
(1, 4)
(1, ∞)

Last edited by KerimF (2024-03-09 21:20:25)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Find Domain of Functions...2

I'd not met the backwards square bracket notation.  But, if it means the same as a round bracket then that's fine.

This crops up all the time in maths; there's no absolute authority to appeal to.  I use Wolfram Alpha but there's no rule book for anything. 

Bob

---

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

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 166

Re: Find Domain of Functions...2

I'd not met the backwards square bracket notation.  But, if it means the same as a round bracket then that's fine.

This crops up all the time in maths; there's no absolute authority to appeal to.  I use Wolfram Alpha but there's no rule book for anything. 

Bob

So, nothing prevents this forum to have its own rule book for math so that its members can understand each other properly when they write certain math's notations.
Naturally, those in charge of this forum may like to start doing such a rule book (then updating it with time) and let it be available to all.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Find Domain of Functions...2

Sorry, but life is too short.  We'd never get passed:

Bob

---

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...2

The convention is square brackets if an end point is included and a round bracket if it's not.

As you cannot reach infinity and it doesn't obey the usual rules for numbers it is not regarded as a number.

So 1 isn't included or you have division by zero; infinity isn't included thus (1, ∞)

Bob

True statement.