Find domains of (X+5)/(2-x), Square root (8-x)

[koreanstar88]

Find the domains.

1) f(x) =(X+5)/(2-x)

I found out that the answer is (-infinity, 2) union (2, infinity), but I don't understand why the first part is (-infinity, 2). That means that the number has to be less than 2 to be a real number?

2) f(x) = Square root (8-x)
how do you know when the use negative infinity along with positive infinity?

is it necessary to graph it to figure it out?
because when i graph it i can get the answer, but just with math i can't seem to figure it out?

Please inform me about domains and these problems PLEASE! THANK YOU!!

 

[pka]

Re: DOMAIN HELP! Please? Thank you

Find the domains. f(x) =(X+5)/(2-x)
I found out that the answer is (-infinity, 2) union (2, infinity), but I don't understand why the first part is (-infinity, 2). That means that the number has to be less than 2 to be a real number?

We cannot divide by zero. So we cannot have x=2. So 2 is the only number not in the domain: \(\displaystyle \Re \backslash \left\{ 2 \right\} = \left( { - \infty ,2} \right) \cup \left( {2,\infty } \right)\).
x can be any number but 2.

Find the domains.
f(x) = Square root (8-x)
how do you know when the use negative infinity along with positive infinity?

We are not allowed to have the square root of a negative number.
So \(\displaystyle 8 - x \ge 0\quad \Rightarrow \quad 8 \ge x\quad \Rightarrow \quad x \in \left( {-\infty , 8 } \right]\).

 

[stapel]

Please inform me about domains and these problems

To learn how to find the domains of functions, please try some of the many lessons available online:

. . . . .Google results for "find domain functions"

Have fun!

Eliz.

 

[koreanstar88]

Re: DOMAIN HELP! Please? Thank you

Find the domains. f(x) =(X+5)/(2-x)
I found out that the answer is (-infinity, 2) union (2, infinity), but I don't understand why the first part is (-infinity, 2). That means that the number has to be less than 2 to be a real number?

We cannot divide by zero. So we cannot have x=2. So 2 is the only number not in the domain: \(\displaystyle \Re \backslash \left\{ 2 \right\} = \left( { - \infty ,2} \right) \cup \left( {2,\infty } \right)\).
x can be any number but 2.

Find the domains.
f(x) = Square root (8-x)
how do you know when the use negative infinity along with positive infinity?

We are not allowed to have the square root of a negative number.
So \(\displaystyle 8 - x \ge 0\quad \Rightarrow \quad 8 \ge x\quad \Rightarrow \quad x \in \left( {-\infty , 8 } \right]\).

how do i know that the square root = 8-x>= 0?

 

[stapel]

how do i know that the square root = 8-x>= 0?

You know this because you know that...

We are not allowed to have the square root of a negative number.

Eliz.