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

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

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domain of sqrt((4-t^2)/(5-3t-2t^2))

domain

\frac{4 - t ^{2}}{5 - 3 t - 2 t ^{2}}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

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

Combine real regions and undefined points for final function domain

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

f (x) = x^{3} - 3 x^{2} - 9 x + 10

y = 3 x - 7

3 x + y = 10

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

f (x) = \frac{( 6 - 2 x ^{2} )}{( x ^{2} - 16 )}

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