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

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

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

domain

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

3 \leq x < 5 or x > 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq 3

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

3 \leq x < 5 or x > 5

f (x) = 7^{x} + 4

x + sin (x)

f (x) = \frac{3}{2} x^{4}

sin (x)

(30 cos (3 5^{\circ}), 30 sin (3 5^{\circ})), (0, 0)

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