What is the domain of f(x)=sqrt(3x-5)+x/(x-6) ?

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

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domain of f(x)=sqrt(3x-5)+x/(x-6)

domain

f (x) = 3 x - 5 + \frac{x}{x - 6}

\frac{5}{3} \leq x < 6 or x > 6

Interval Notation

[\frac{5}{3}, 6) \cup (6, \infty)

Solution steps

Find non-negative values for radicals:

x \geq \frac{5}{3}

Find undefined (singularity) points:

x = 6

Combine real regions and undefined points for final function domain

\frac{5}{3} \leq x < 6 or x > 6

f (x) = sinh (x)

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

lo g_{3} (x^{2} - 4)

- m + 12 - m

f (x) = \frac{1}{4} x

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