What is the domain of (x-sqrt(x+2))/(sqrt(4x+1)-3) ?

The domain of (x-sqrt(x+2))/(sqrt(4x+1)-3) is -1/4 2

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domain of (x-sqrt(x+2))/(sqrt(4x+1)-3)

domain

\frac{x - x + 2}{4 x + 1 - 3}

- \frac{1}{4} \leq x < 2 or x > 2

Interval Notation

[- \frac{1}{4}, 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - \frac{1}{4}

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

- \frac{1}{4} \leq x < 2 or x > 2

4 ln (3) \cdot 9^{x^{2}} x

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

f (x) = - 2 x^{3} + 6 x^{2} + 12

f (x) = 2 x + x - x^{2}

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

What is the domain of (x-sqrt(x+2))/(sqrt(4x+1)-3) ?
The domain of (x-sqrt(x+2))/(sqrt(4x+1)-3) is -1/4 <= x<2\lor x>2