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

The domain of f(x)=(sqrt(x))/(2-x) is 0 2

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

domain

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

0 \leq x < 2 or x > 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq 0

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

0 \leq x < 2 or x > 2

\frac{2 x ^{2} - 4}{3 x ^{2} + 6 x - 45}

y = 2 + x - x^{2}

- x^{2} + 4

{sin (x) : x < 0, 2 x : x \geq 0}

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

What is the domain of f(x)=(sqrt(x))/(2-x) ?
The domain of f(x)=(sqrt(x))/(2-x) is 0<= x<2\lor x>2