What is the domain of f(x)=(sqrt(x-2))/(4-x) ?

The domain of f(x)=(sqrt(x-2))/(4-x) is 2 4

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domain of f(x)=(sqrt(x-2))/(4-x)

domain

f (x) = \frac{x - 2}{4 - x}

2 \leq x < 4 or x > 4

Interval Notation

[2, 4) \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 2

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

2 \leq x < 4 or x > 4

f (x) = x^{2} + 5 x + 4

x^{3} - 12 x + 1

y = 7

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

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

What is the domain of f(x)=(sqrt(x-2))/(4-x) ?
The domain of f(x)=(sqrt(x-2))/(4-x) is 2<= x<4\lor x>4