What is the domain of 9(x)sqrt((x-5)/(x-7)) ?

The domain of 9(x)sqrt((x-5)/(x-7)) is x 7

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domain of 9(x)sqrt((x-5)/(x-7))

domain

9 (x) \frac{x - 5}{x - 7}

x \leq 5 or x > 7

Interval Notation

(- \infty, 5] \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 5 or x > 7

Find undefined (singularity) points:

x = 7

Combine real regions and undefined points for final function domain

x \leq 5 or x > 7

\frac{- 3 x ^{2} + 24 x - 45}{2 x ^{2} - 10 x}

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

f (x) = \frac{5 x}{x + 6}

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

f (x) = 5 x^{2} + 9

What is the domain of 9(x)sqrt((x-5)/(x-7)) ?
The domain of 9(x)sqrt((x-5)/(x-7)) is x<= 5\lor x>7