What is the domain of f(x)=(sqrt(x-5))/(3x-18) ?

The domain of f(x)=(sqrt(x-5))/(3x-18) is 5 6

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domain of f(x)=(sqrt(x-5))/(3x-18)

domain

f (x) = \frac{x - 5}{3 x - 18}

5 \leq x < 6 or x > 6

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq 5

Find undefined (singularity) points:

x = 6

Combine real regions and undefined points for final function domain

5 \leq x < 6 or x > 6

f (x) = x^{2} + 300 x - 100000

y = x - 8

f (x) = - 2 1 - x

+ (- \frac{1}{6}) x^{2} + 200 x

y = \frac{1}{x} + 3

What is the domain of f(x)=(sqrt(x-5))/(3x-18) ?
The domain of f(x)=(sqrt(x-5))/(3x-18) is 5<= x<6\lor x>6