What is the domain of f(x)=(sqrt(x-6))/(x(x-7)) ?

The domain of f(x)=(sqrt(x-6))/(x(x-7)) is 6 7

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domain of f(x)=(sqrt(x-6))/(x(x-7))

domain

f (x) = \frac{x - 6}{x ( x - 7 )}

6 \leq x < 7 or x > 7

Interval Notation

[6, 7) \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 6

Find undefined (singularity) points:

x = 0, x = 7

Combine real regions and undefined points for final function domain

6 \leq x < 7 or x > 7

f (x) = \frac{5}{( x - 3 )}

f (x) = 2 x + 1 - 3

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

(x - 1)^{2} + 2

f (x) = x + x + 1

What is the domain of f(x)=(sqrt(x-6))/(x(x-7)) ?
The domain of f(x)=(sqrt(x-6))/(x(x-7)) is 6<= x<7\lor x>7