What is the domain of sqrt((x^2+4x-21)/(x-2)) ?

The domain of sqrt((x^2+4x-21)/(x-2)) is -7 = 3

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domain of sqrt((x^2+4x-21)/(x-2))

domain

\frac{x ^{2} + 4 x - 21}{x - 2}

- 7 \leq x < 2 or x \geq 3

Interval Notation

[- 7, 2) \cup [3, \infty)

Solution steps

Find non-negative values for radicals:

- 7 \leq x < 2 or x \geq 3

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

- 7 \leq x < 2 or x \geq 3

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

f (x) = \frac{- 2 x + 6}{3}

arccos (2 x) \cdot ln (x^{2})

f (x) = \frac{2}{x ^{2} + 2 x - 24}

\frac{( x ^{2} - 2 x )}{x ^{2} + x - 6}

What is the domain of sqrt((x^2+4x-21)/(x-2)) ?
The domain of sqrt((x^2+4x-21)/(x-2)) is -7<= x<2\lor x>= 3