What is the domain of f(x)=(sqrt(x-2))/(sqrt(x+1)-2) ?

The domain of f(x)=(sqrt(x-2))/(sqrt(x+1)-2) is 2 3

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domain of f(x)=(sqrt(x-2))/(sqrt(x+1)-2)

domain

f (x) = \frac{x - 2}{x + 1 - 2}

2 \leq x < 3 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq 2

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

2 \leq x < 3 or x > 3

f (x) = \frac{1}{2} ln (3 - x^{2})

\frac{x ^{2} - 2 x}{x - 6}

x^{2} 3 x - 5

\frac{x - 5}{2 x + 4}

f (x) = lo g_{e} (x)

What is the domain of f(x)=(sqrt(x-2))/(sqrt(x+1)-2) ?
The domain of f(x)=(sqrt(x-2))/(sqrt(x+1)-2) is 2<= x<3\lor x>3