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

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

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

domain

f (x) = \frac{3 x + 2}{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) = - \frac{1}{3} x - 6

y = \frac{x ^{2} + 1}{x}

f (x) = e^{x + 1} - 1

(- 3, 0), (0, - 2)

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

What is the domain of f(x)=(3x+2)/(sqrt(x^2-7x)) ?
The domain of f(x)=(3x+2)/(sqrt(x^2-7x)) is x<0\lor x>7