What is the domain of f(x)=(sqrt(x)+1)/(x^2-4) ?

The domain of f(x)=(sqrt(x)+1)/(x^2-4) is 0 2

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domain of f(x)=(sqrt(x)+1)/(x^2-4)

domain

f (x) = \frac{x + 1}{x ^{2} - 4}

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, x = - 2

Combine real regions and undefined points for final function domain

0 \leq x < 2 or x > 2

\frac{x + 1}{10 ( x - 2 )}

(- 1, 2), (3, 2)

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

\frac{x ^{2}}{1 - x}

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

What is the domain of f(x)=(sqrt(x)+1)/(x^2-4) ?
The domain of f(x)=(sqrt(x)+1)/(x^2-4) is 0<= x<2\lor x>2