What is the domain of y=sqrt((x^2+3x-4)/(6-x-x^2)) ?

The domain of y=sqrt((x^2+3x-4)/(6-x-x^2)) is -4<= x<-3\lor 1<= x<2

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domain of y=sqrt((x^2+3x-4)/(6-x-x^2))

domain

y = \frac{x ^{2} + 3 x - 4}{6 - x - x ^{2}}

- 4 \leq x < - 3 or 1 \leq x < 2

Interval Notation

[- 4, - 3) \cup [1, 2)

Solution steps

Find non-negative values for radicals:

- 4 \leq x < - 3 or 1 \leq x < 2

Find undefined (singularity) points:

x = - 3, x = 2

Combine real regions and undefined points for final function domain

- 4 \leq x < - 3 or 1 \leq x < 2

f (x) = - 8 + \frac{1}{2} x

f (x) = 2 x - 3 + 5

f (x) = 3 - 5 x

f (x) = tan (x) + cot (x)

f (x) = 2000 x - 10000

What is the domain of y=sqrt((x^2+3x-4)/(6-x-x^2)) ?
The domain of y=sqrt((x^2+3x-4)/(6-x-x^2)) is -4<= x<-3\lor 1<= x<2