What is the domain of f(x)=x^2-x +5

Question

jim_thompson5910 · Answer

This is a polynomial.

All polynomials have the same domain: the set of real numbers (since you can plug in any real number for x and get some real number out for y or f(x))

So the domain of f(x) is the set of all real numbers.

anonymous · Answer

Okay can you explain how to solve this problem because I really have no clue.

jim_thompson5910 · Answer

It's already solved and answered

jim_thompson5910 · Answer

Now sure what you're looking for exactly

anonymous · Answer

Okay what if I had a problem that said what is the domain of f(x)=1/-X+3. What would be the answer? Could you explain more.

jim_thompson5910 · Answer

You cannot divide by zero

So -x+3 cannot be zero

This means that x cannot be 3 (since this makes -x+3 equal to 0)

So the domain is the set of all real numbers BUT x cannot equal 3.

jim_thompson5910 · Answer

I'm assuming the problem is $$\Large f(x) = \frac{1}{-x+3}$$

anonymous · Answer

Yes thats it.

anonymous · Answer

Im confused.. why zero?

anonymous · Answer

If x cannot equal to zero then what is it?

jim_thompson5910 · Answer

because you can't divide by zero

jim_thompson5910 · Answer

no, x cannot equal 3

jim_thompson5910 · Answer

x can be any number but 3

anonymous · Answer

Ok, if you cannot divide by zero then what do you divide by?

jim_thompson5910 · Answer

you can divide by any number but zero

jim_thompson5910 · Answer

ex: 2/1 = 2

2/0.5 = 4

but 2/0 is undefined

anonymous · Answer

Okay I understand that. So 1/-x+3 would be?

anonymous · Answer

undefined?

jim_thompson5910 · Answer

it's only undefined when x = 3

jim_thompson5910 · Answer

otherwise, it's some number

anonymous · Answer

Ok.. well back to the first problem. It asks me to find the domain of f(x)= x^2-x+5. But it doesn't tell me what x is, When I solved it I got this... f(x)= -5 Can you please help me with this problem.

jim_thompson5910 · Answer

but the domain of any polynomial is the set of all real numbers

jim_thompson5910 · Answer

there has to be more to this

anonymous · Answer

There isn't. Thats all to the problem.. I have 5 problems like that.

jim_thompson5910 · Answer

hmm not sure then

jim_thompson5910 · Answer

it sounds like you're either solving for x or evaluating x for a specific value

but you're not finding the domain if it's f(x) = -5

jim_thompson5910 · Answer

because the domain again is simply "the set of all real numbers"

anonymous · Answer

Im not sure if thats the answer. i just tried to solve it..
f(x)= x^2-x=5
-5=x^2-x
-5=x

jim_thompson5910 · Answer

then I would go with "the set of all real numbers" if all they want is the domain

anonymous · Answer

f(x)= x^2-x+5
-5=x^2-x
-5=x

jim_thompson5910 · Answer

esp if this a polynomial

anonymous · Answer

Okay so if I had a problem like f(x)=1/radical x-3 it would be a set of all real numbers?

jim_thompson5910 · Answer

no, because we now have a division by a variable expression

jim_thompson5910 · Answer

there's a potential to divide by zero

anonymous · Answer

Okay how would I figure this out? so I divide what by zero?

jim_thompson5910 · Answer

The problem is $$\Large f(x) = \frac{1}{\sqrt{x-3}}$$ right?

anonymous · Answer

Yes!

jim_thompson5910 · Answer

ok so the denominator cannot be zero

jim_thompson5910 · Answer

if it were, then

sqrt(x-3) = 0

x - 3 = 0

x = 3

This means that when x = 3, the denominator is zero.

This means that you can plug in any other number BUT x = 3 into the function

So the domain is the set of all real numbers but x can't equal 3.

anonymous · Answer

so the answer can be anything but not 3?

jim_thompson5910 · Answer

yes that's one way of stating the domain

jim_thompson5910 · Answer

it's probably a more compact way to state what numbers are excluded from the domain (which is x = 3)

anonymous · Answer

she's looking for interval notation when x does not equal zero, you cant have zero in the denominator, so your domain is (-infinity,0] U [0, infinity)