What is the domain of f(x)=(sqrt(x-2))/(2x-10) ?

The domain of f(x)=(sqrt(x-2))/(2x-10) is 2 5

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domain of f(x)=(sqrt(x-2))/(2x-10)

domain

f (x) = \frac{x - 2}{2 x - 10}

2 \leq x < 5 or x > 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq 2

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

2 \leq x < 5 or x > 5

f (x) = 2 x - 18

f (x) = x

2 (x + 1)^{2} - 5

x^{3} - 48 x

f (x) = \frac{x - 2}{x ^{2} + 2 x - 15}

What is the domain of f(x)=(sqrt(x-2))/(2x-10) ?
The domain of f(x)=(sqrt(x-2))/(2x-10) is 2<= x<5\lor x>5