What is the domain of sqrt((-x^2+7x-10)/(x-3)) ?

The domain of sqrt((-x^2+7x-10)/(x-3)) is x<= 2\lor 3<x<= 5

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domain of sqrt((-x^2+7x-10)/(x-3))

domain

\frac{- x ^{2} + 7 x - 10}{x - 3}

x \leq 2 or 3 < x \leq 5

Interval Notation

(- \infty, 2] \cup (3, 5]

Solution steps

Find non-negative values for radicals:

x \leq 2 or 3 < x \leq 5

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x \leq 2 or 3 < x \leq 5

f (x) = 1 - \frac{x ^{2}}{16}

f (x) = \frac{1 - 3 x}{x ^{3} - 4 x ^{2} - 5 x}

\frac{\frac{2}{x}}{\frac{4}{x + 4}}

f (x) = (x - 1)^{(2)} + 3

3 w (2 - 3 u) = 6 u - 3

What is the domain of sqrt((-x^2+7x-10)/(x-3)) ?
The domain of sqrt((-x^2+7x-10)/(x-3)) is x<= 2\lor 3<x<= 5