Question

Please help!

What is the domain of g(x)=|x|/x^2?

How do I find f(2+h), f(x+h), and [f(x+h)-f(x)]/h where h is not equal to zero, given that f(x)= x-x^2?

Answer 1

x can not be 0

Answer 2

@sourwing why not?

Answer 3

0^2 = 0 and you can't devide by 0

Answer 4

The domain is all possible values that can be input into a function. Normally it is all numbers, but in some cases (division by zero, negative under radical) certain numbers cannot be input into the function.

Looking at your function, are there any values for x that would cause an undefined operation?

Answer 5

@sourwing but since the numerator is also zero, I thought it wouldn't matter, because it'd just be 0...?

Answer 6

@jollyjolly0 it's be negative numbers, right?

Answer 7

You are allowed to put a negative value of x into absolute value. In fact, that's just about the only thing it's good for!

Answer 8

0/0 is indeterminate. It has no meaning. In general, anything divided by 0 is a no no in math.

Answer 9

So, then the domain would be all real numbers except for 0?

Answer 10

Yup!

Answer 11

How would I graph that, though?

Answer 12

Well, for graphing absolute values, you typically break it into 2 cases. For example, y=|x|
If you say x is always positive, then the above becomes
y=x
If you say x is always negative, then it simplifies to
y = -x

Basically, you just break it into 2 cases.

Answer 13

One case where the absolute value does nothing (in that case, all positive x) and one case where it makes its contents negative (in that case, all negative x)

Answer 14

Got it. Thank you!!

Do you think you can help me with my other question?

Answer 15

Ok, so the given function f(x) = x - x^2
Basically, the f(something) notation means that you replace x with something in the original equation, f(x).

For example, f(3) = 3 - 3^2 = -6
so for f(2+h), we replace the "x"s with "(2+h)"s. You can probably take it from there.

the other questions all follow a similar form, so you should be able to get them. Let me know if you get stuck though =)

Answer 16

I got it! Thank you!

Answer 17

No problem! One last thing,

Let me real quick try to explain the reason why 0/0 is indeterminate (I gave kinda a crap answer earlier)

First, say I have a fraction 0/10
and lets also say that that I don't know what the fraction equals, so I just say say it equals x. That gives,
0/10 = x
If i multiply both sides by 10, I get
0 = 10x
That means x must equal 0, otherwise the equation wouldn't be true! Because x = the fraction, the fraction equals 0 as well.

Now lets say I have 0/0
Again, lets say it equals some number x, so
0/0 = x
If i multiply by the denominator we get
0 = 0 * x
This tells me nothing! x could literally me any number and the equation would still be true! That is why mathematicians say 0/0 is "indeterminate", becasue it could be anything.

Try to enjoy math and understand the reasons behind it. You will find it both easier and enjoyable =)

Answer 18

This is a great explanation! Thank you so much!