What is the domain of y=(sqrt(3x+5))/(x-1) ?

The domain of y=(sqrt(3x+5))/(x-1) is -5/3 1

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domain of y=(sqrt(3x+5))/(x-1)

domain

y = \frac{3 x + 5}{x - 1}

- \frac{5}{3} \leq x < 1 or x > 1

Interval Notation

[- \frac{5}{3}, 1) \cup (1, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - \frac{5}{3}

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

- \frac{5}{3} \leq x < 1 or x > 1

f (x) = x - 3 x^{\frac{2}{3}}

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

f (x) = ln (5 x - 8)

f (x) = \frac{x ^{2} - x - 2}{x ^{2} - 6 x + 8}

1 - 2 + x

What is the domain of y=(sqrt(3x+5))/(x-1) ?
The domain of y=(sqrt(3x+5))/(x-1) is -5/3 <= x<1\lor x>1