Question

I need help with answering the following problem: State the domain and range for the following. Find when f(x)=0.
f(x)= (x+2)/(5x-10)

Answer 1

Since f(x)=(x+2)/(5x+10) is the same thing as y=(x+2)/(5x+10)
Domain = x and range = y. If you graph it, domain (negative infinity, negative 2) union (-2, positive infinity) and range is all real numbers.

Answer 2

The domain is also except when x = -2 because that would make the denominator undefined.

Answer 3

the domain is: 5x+10=0 x=-2 is impossible
range i the domain of the inverse
\[5xy+10y=x+2\rightarrow f^-1(x) \frac{ 2-10x }{5x-1 }\] so x=1/5 is impossible

Answer 4

I.e the domain R-{-2}
range R-{1/5}

Answer 5

i got the domain part maybe you can explain the range more in depth? and why isn't the range just all real numbers?

Answer 6

you have f(x) represented by the point in the plane (x,f(x)) the inverse when we solve for f(x) , I mean we try to find the point (f(x),x) ,so if we tried to find the entire domain of the inverse we get the range and that's what just happened

Answer 7

anyways try to plug f(x)=1/5 and see
\[\frac{ x+2 }{ 5x-10 }=1/5 \rightarrow x-2=x+2\] and that's impossible dude !!

Answer 8

should i have mentioned that I'm a senior at a public school with 1 day of being in AP calc, explain it to me like i'm an idiot, because i'm still a calc virgin

Answer 9

wait nvm i got it

Answer 10

thanks!

Answer 11

How about f(x)=4/1-x ?

Answer 12

lol even I didn't understand what you said about yourself , but I'm glad you got it after all :)