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

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

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

domain

f (x) = \frac{2 x + 7}{x - 3}

- \frac{7}{2} \leq x < 3 or x > 3

Interval Notation

[- \frac{7}{2}, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - \frac{7}{2}

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

- \frac{7}{2} \leq x < 3 or x > 3

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