What real values of x are not in the domain of $f(x) = \frac{1}{|x^2 + 3x - 4| + |x^2 + 9x - 10|}$?
+130070 The denominator cannot = 0
Note that l x^2 + 3x + 4 l = l (x -1) ( x + 4) l
And l x^2 + 9x -10 l = l (x -1) ( x + 10) l
So we have
l (x -1) ( x + 4) l + l (x -1) ( x + 10 l =
( l x - 1 l ) ( l (x + 4) l + l x + 10 l )
The only value of x that makes this 0 is when x = 1
So .....x =1 is not in the domain
