Pre calc
posted by Katie S on .
Find the Domain of the function:
f(x)=the square root of the entire fraction x^2+6x16 over x^22x15

domain is your choice of x's you can use
First of all the bottom cannot be zero
so
x^2  2x  15 ≠ 0
(x5)(x+3) ≠ 0
x≠5 or x≠ 3
Secondly the entire expression cannot be negative, because of the square root part
it simplifies to
(x+8)(x2)/((x5)(x+3)
clearly any x<8 and x> 5 are ok
also the expression is positive between 3 and 2
it is negative between 8 and 3, as well as 2 to 5
I will let let you summarize the above.
Make a number line , put those critical values on and mark the line accordingly