Finding the domain of a function?

Question

f(x)= (2x+7)/(x^2-13x-30)

10 points for teaching me how.

I don't want just the answer, because I'd like to understand it for the test.

Answer 1

Simply ask yourself what values of x will not work.

ie if you have a square root sign, values that cause the part under the square root to be negative won't work.

if you have a fraction, values that cause the denominator to equal 0 don't work because we can't divide by 0.

So in your case values of x that don't work are values that cause

x²-13x-30 = 0

(x-15)(x+2) = 0

x = 15 and x = -2 will cause the function to have problems

So your answer is

all real numbers except x = 15 and x = -2

or

x<-2 U -2<x<15 U 15<x

or

(-∞,-2) U (-2,15) U (15, ∞)

Answer 2

well

it's kinda easy, lol

first look at the 2x+7

it's domain wold be from neg. infinite to pos. infinite

then look at the x^2-13x-30

since it's in the denominator of the fuction, you cant have any number that equals to zero, as it would tending to infinite.

so we put x^2-13x-30 = 0

be factorize it to

(x+15) (x-2)<--- if you want this explain send me a pm.

ok then now we have -15 and 2 when we insolate the x from the previous thing, lol

so the domain can be any numbre except -15 and to

so you write it like this

(neg. infinite,-15) U (-15,2) U (2, infinite)

Peace, any other question regarding this, please fell free to pm me.