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

Algebra ->  Algebra  -> Functions -> 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       Log On

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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(21667) About Me  (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 ?"


f%28x%29=%28x%2B4%29%2F%28x%29 Start with the given function


x=0 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 x=0 makes the denominator equal to zero, this means we must exclude x=0 from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except x%3C%3E0

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:

drawing%28500%2C50%2C-10%2C10%2C-10%2C10%2C%0D%0Anumber_line%28+500%2C+-10%2C+10%29%2C%0D%0Ablue%28arrow%280.2%2C-7%2C10%2C-7%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6.5%2C10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6%2C10%2C-6%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5.5%2C10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5%2C10%2C-5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-7%2C-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6.5%2C-10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6%2C-10%2C-6%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5.5%2C-10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5%2C-10%2C-5%29%29%2C%0D%0A%0D%0Acircle%280%2C-5.8%2C0.35%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%0D%0A%29 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 x=0 (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 f%283%29

f%28x%29=4-x-x%5E2 Start with the given polynomial


f%283%29=4-%283%29-%283%29%5E2 Plug in x=3


f%283%29=4-3-9 Square 3 to get 9

f%283%29=-8 Now combine like terms


So when x=3, f%28x%29=-8



So you are correct on both of them