Math Is Fun Forum

Deon588

Member

Registered: 2011-05-02

Posts: 68

Domain of a function and equation

Hi all.  My question is: find the domain of g(x) and solve the equation 4^g(x)=8 am I doing this the right way?  I feel very unsure about the domain.  Thanks in advance.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Domain of a function and equation

Hi Deon588;

Welcome to the forum.

Did you plug in your answer after you were done? x = - 1 / 10 gives an answer of more than 17 which is not 8.

Also why did you not graph the function? There are many good graphers online. That would have showed you the approximate position of the roots and the possible domain of g(x). Here is one:

http://www.mathsisfun.com/data/function … 29&func2=2

Let's work the problem starting as you have done.

Can you solve from here? Do you need help?

For the domain part.

The domain is the numbers you can put into a function. All the numbers that work.

http://www.mathsisfun.com/sets/domain-r … omain.html

Can you really find any real x that g(x) is complex for, or does not exist for?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: Domain of a function and equation

hi Deon588 and bobbym

Odd?

Isn't this just

or

if we allow a negative root as well.

It seems unlikely to me that g(x) would have been defined like this.  Can we check the definition of g please?

Bob

Last edited by Bob (2011-06-12 18:17:50)

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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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Domain of a function and equation

Hi Bob;

I thought it was:

The problem with the other move is, I got killed with this once...

Only in some cases does it equal. When x is complex it does not always hold. That is why I avoided making that move. Could have been done here because we are working only with reals. But it is kind of habit of mine to avoid that simplification. Either way it should yield the same two roots that the quadratic I left the OP with does.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Deon588

Member

Registered: 2011-05-02

Posts: 68

Re: Domain of a function and equation

Hi bobby and bobbym.  Bobby I double checked and no the definition of g(x) is as I wrote it.  Bobbym That makes total sense now squaireing both sides I thought it looked like I should use that method.  As for the Graphing I have Geogebra but I doubt that i would be aloud to use that during my exam.  So the domain is just R?  Can you please explain to me how to find the domain without graphing the equation?
Thanks a lot
Deon

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Domain of a function and equation

Hi Deon588;

I always graph the equation for roots and everything else. Here it is just obvious. In order to find the real numbers that will not be in the domain. You check for 2 things. Zeroes in the denominators, does not apply here and - values inside the radical. Here everything in the radical must be positive because of the square.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Deon588

Member

Registered: 2011-05-02

Posts: 68

Re: Domain of a function and equation

Thanks that helps a lot.  I am doing a mathematics access course at my university which is basically all high school math in 1 year so even the obvious things seems complicated to me at this stage lol.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Domain of a function and equation

Hi;

Keep working at it. It will get easier. Good luck with your course.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: Domain of a function and equation

hi Deon588 and bobbym

Whoops

was just a typo.  I meant

But the rest of my comment is still valid, I think.

I've been out on a first aid course all day, but I did give this problem some more thought on the way and this is what I've come up with:

I'll start with the domain.

When a mathematician defines a function it consists of two parts

(i)  the number crunching bit eg. f(x) = sinx or g(x) = logx

(ii) the domain that this number crunching should be applied to (eg x is real or x < 0 etc)

This responsibility lies with the questioner not the student.  You can no more expect the student to know what domain to use than you can expect to solve an equation if you are not told what the equation is.

This is not a trivial point.  Consider the function 

I could specify x ∈ {square numbers}

Perfectly reasonable ... the range would be {+ve integers}

or I could have x ∈ {reals : x ≥ 0}
in which case the range is the same set

or I could have x ∈ {complex numbers}etc, etc

How can you ask a question where the student has to guess which of these is the one intended?

In some less rigorous mathematical areas, details like this are sometimes left out as 'obvious'  ; but this is real analysis.  The utmost rigor is required so the questioner should be setting a good example by saying exactly what they mean.

The question makes better sense if it is

because then you can ask

"If the domain is intended to be as large a subset of the reals as can be, what should this domain be?"

As negative numbers cannot be rooted this would add the restriction x ≤ 2.  Is that what this questioner really wants?

Then the equation

makes sense too.

As 4 to the power 3/2 makes 8 that gives us

so

Don't know if any of this helps, but I feel a lot better for getting it off my chest. 

Bob

Last edited by Bob (2011-06-13 05:11:03)

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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