What is the domain of 1/(sqrt(x^2-7x)) ?

The domain of 1/(sqrt(x^2-7x)) is x 7

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domain of 1/(sqrt(x^2-7x))

domain

\frac{1}{x ^{2} - 7 x}

x < 0 or x > 7

Interval Notation

(- \infty, 0) \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 0 or x \geq 7

Find undefined (singularity) points:

x = 7, x = 0

Combine real regions and undefined points for final function domain

x < 0 or x > 7

f (x) = x^{2} e^{- x^{2}}

f (x) = - 6 x^{3} + 9 x^{2} + 36 x

(- 2, - 6), (- 5, 0)

f (x) = 3 x^{4} + 12 x

f (x) = - 3 (4 - x) (4 x + 3)

What is the domain of 1/(sqrt(x^2-7x)) ?
The domain of 1/(sqrt(x^2-7x)) is x<0\lor x>7