What is the domain of f(x)=sqrt((4-x^2)/(5-3x-2x^2)) ?

The domain of f(x)=sqrt((4-x^2)/(5-3x-2x^2)) is x = 2

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domain of f(x)=sqrt((4-x^2)/(5-3x-2x^2))

domain

f (x) = \frac{4 - x ^{2}}{5 - 3 x - 2 x ^{2}}

x < - \frac{5}{2} or - 2 \leq x < 1 or x \geq 2

Interval Notation

(- \infty, - \frac{5}{2}) \cup [- 2, 1) \cup [2, \infty)

Solution steps

Find non-negative values for radicals:

x < - \frac{5}{2} or - 2 \leq x < 1 or x \geq 2

Find undefined (singularity) points:

x = - \frac{5}{2}, x = 1

Combine real regions and undefined points for final function domain

x < - \frac{5}{2} or - 2 \leq x < 1 or x \geq 2

What is the domain of f(x)=sqrt((4-x^2)/(5-3x-2x^2)) ?
The domain of f(x)=sqrt((4-x^2)/(5-3x-2x^2)) is x<-5/2 \lor-2<= x<1\lor x>= 2