Question

describe the domain of the following function f(x)=-6x+4
f(x)=sqrt10-x

Answer 1

Domain of a line is all real numbers, unless its vertical

Answer 2

can you tell that just by looking at it?

Answer 3

Yes f(x)=mx+b is the form of a line, x=a is the form of a vertical line. So for the first one its all real numbers

Think of it like this, you can plug any integer, positive or negative into -6x+4 and get an integer out

Answer 4

because even if x = 0 then you still get 4?

Answer 5

Yep you can plug in all real numbers and you will get a real number output.

for the second one is it

\[\sqrt{10-x}\]

Answer 6

what does "no domain restrictions" mean?

Answer 7

What i just said, you can plug in all real numbers and you will get a real number output

Answer 8

oh ok. gotcha. thanks

Answer 9

For the second one, under the square root has to be greater than or equal to 0

so to find the domain solve this little inequality

\[10-x \ge0\]

Answer 10

x=10, so it is \[\ge 0\]

Answer 11

or actually I didnt do that right.

Answer 12

in fact I did it quite opposite didn't I?

Answer 13

x=-10

Answer 14

maybe I'm getting ahead of myself. I forgot that I divided out a -1 from the -10 which is x=10

Answer 15

Its an inequality not an equation

so first subtract 10 from both sides to get

\[-x \ge -10\]

Answer 16

then divide by -1, which flips the inequality sign

\[x \le 10\]

Answer 17

oh, so when you divide the neg 1 (or any number?) from the x to the 10 you flip the sign. I always forget that rule

Answer 18

Yeah just gotta burn it in your brain. When you divide or multiply by a negative number it flips the inequality

so your domain is all x less than or equal to 10

Answer 19

or ( -\[\infty \],10]

Answer 20

that didn't format right, but you get me.

Answer 21

Yes thats correct
\[(-\infty,10]\]

Answer 22

what if it's g(x)= \[\frac{ 1 }{ x^{2}+4x-5 }\]

Answer 23

You cant divide by 0, so set the denominator equal to 0 and solve. What you get will be the values that arent in the domain

Answer 24

ok, after I get it to x^2+4x-5 I do the quadratic formula?

Answer 25

or, complete the square I mean...

Answer 26

Use whatever method you like best.

It factors easy though
(x-1)(x+5)=0

Answer 27

gotcha, ok. cool

Answer 28

you wouldn't happen to know of a good site with a listing of all these rules for the domains would you?

Answer 29

if not, I think I have them in my notes, I'll find them and look over it. thanks for your help!

Answer 30

Hmm, you could try googling it. But basically, if theres a square root involved, you know under the square root has to be 0 or positive.

if there's a fraction you know the denominator cant be 0, things like that

Answer 31

ok, thanks again