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

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

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

domain

f (x) = \frac{x ^{2} + 2 x - 3}{4 - x ^{2}}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

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

f (x) = \frac{- 5 x + 3}{x ^{2} - 3 x - 40}

f (x) = 10 x^{2} + 9 x + 100

y = \frac{- 7}{( x - 2 ) ^{2}}

f (x) = \frac{2}{2 + 5 x}

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