What is the domain of (sqrt(1-2x))/(sqrt(3-2x-x^2)) ?

The domain of (sqrt(1-2x))/(sqrt(3-2x-x^2)) is -3<x<= 1/2

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domain of (sqrt(1-2x))/(sqrt(3-2x-x^2))

domain

- 3 < x \leq \frac{1}{2}

Interval Notation

(- 3, \frac{1}{2}]

Solution steps

Find non-negative values for radicals:

- 3 \leq x \leq \frac{1}{2}

Find undefined (singularity) points:

x = - 3, x = 1

Combine real regions and undefined points for final function domain

- 3 < x \leq \frac{1}{2}

What is the domain of (sqrt(1-2x))/(sqrt(3-2x-x^2)) ?
The domain of (sqrt(1-2x))/(sqrt(3-2x-x^2)) is -3<x<= 1/2