Question

What values of x will make f(x) continuous?
1) √5-2x
2) f(x) = index is 3 √2x+5
3) f(x) = 1/x2-x - 6

PLEASE HELP ME!

Answer 1

Please help me. :(

Answer 2

Help!

Answer 3

First of all, what's the requirements to meet for something to be continuous?

Answer 4

I don't really know. This topic is all about continuity at an interval. Looking out for 0 denominators and such.

Answer 5

What you do is you look for values of x for which the function is not defined.
For example, a square root is not defined if something in it is negative (unless you're applying complex numbers which I doubt you'll have to do in your course).

Answer 6

So if you have for example
\[f(x)=\sqrt{5-2x}\]
You look for what values of x is going to make the stuff inside your square root negative.

Answer 7

Do you understand how to go about now? :D

Answer 8

Not yet. :(

Answer 9

Can you solve 'em for me? And explain too if you can. Really having a hard time understanding.

Answer 10

Well, what part do you not understand? I'm not here to solve you your homework/problems but to make you learn how to solve them; ironically as you might think this is -- solving them for you does not make you learn more, rather it makes you learn less.

Answer 11

How about number 1? Why make it negative?

Answer 12

I don't understand your question.

Answer 13

If you're referring to your own first question; the reason you look for where (5-2x) is negative, is because: if (5-2x) is negative your function is not going to be continous.

Answer 14

But you said that I should look for what value of x is going to make the stuff inside my square root negative.

Answer 15

HELP MEEEEEEEEEEE! :(

Answer 16

Yeah so if you have 5-2x, at what interval for x will (5-2x) be negative?

Answer 17

if x=0, you have 5-2*0 which is positive,
if x=1, you have 5-2*1 which still is positive; etc.

Answer 18

I'll give you even more, given that you want 5-2x to be greater or equal to 0; you can form the expression
\[5-2x\geq0\]

Answer 19

And then? How can it be continuous?

Answer 20

Explain your thoughts, please; don't be shy. :D

Answer 21

Um, how do we make it continuous? Our teacher didn't teach us how to. :(

Answer 22

You don't "make" anything continuous, it's either continuous or it's not.
The only general thing you have to remember regarding continuous stuff is that it has to be allowed. Normally this only applies to 1/"something" where something can't ever be 0. And square root("something") where "something" can't be negative.

Answer 23

But the question was, what values of x will make f(x) continuous.

Answer 24

Exactly, when for example:
\[f(x)=\sqrt{x}\]
Your x MUST be GREATER than or equal to 0:
\[x\geq0\]

Answer 25

If it's not, your function is not continuous.

Answer 26

Meaning, in my simple example:
f(x) is continuous if
\[x\geq0\]

Answer 27

So it's going ti be \[5 - 2x \ge 0?\]

Answer 28

This is a step in the right direction, you're not done yet though! You need to isolate x as well.

Answer 29

Like?

Answer 30

You have to end up with x alone on one side of the equation.

Answer 31

\[5 - 2 \ge x?\]

Answer 32

The equality sign is the same thing as = in terms of operations, with the difference that if you multiply with (-1) on both sides, you have to turn your equality sign.

Answer 33

Alright! Thank you!