SOLUTION: What is the domain of the function F given by F(x)=x+4/x ? I think the answer is "all reall numbers except 0" Given f(x)=4-x-x^2 find f(3) I think th answer is f(3)=-8

Question 107467: What is the domain of the function F given by F(x)=x+4/x ?
I think the answer is "all reall numbers except 0"
Given f(x)=4-x-x^2 find f(3)
I think th answer is f(3)=-8
thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"What is the domain of the function F given by F(x)=x+4/x ?"

Start with the given function

Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.

Since makes the denominator equal to zero, this means we must exclude from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except

So our domain looks like this in interval notation

note: remember, the parenthesis excludes 0 from the domain

If we wanted to graph the domain on a number line, we would get:

Graph of the domain in blue and the excluded value represented by open circle

Notice we have a continuous line until we get to the hole at (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal 0

"Given f(x)=4-x-x^2 find f(3)"

Lets evaluate

Start with the given polynomial

Plug in

Square 3 to get 9

Now combine like terms

So when ,

So you are correct on both of them
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