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What real values of x are not in the domain of $f(x) = \frac{1}{|x^2 + 3x - 4| + |x^2 + 9x - 10|}$ ?

Guest Apr 6, 2022

CPhill · Answer 1 · 2022-04-06T08:02:56

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