What is the domain of (x+sqrt(x)(2x^2-5))/(2x^2-5) ?

The domain of (x+sqrt(x)(2x^2-5))/(2x^2-5) is 0 sqrt(5/2)

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domain of (x+sqrt(x)(2x^2-5))/(2x^2-5)

domain

\frac{x + x ( 2 x ^{2} - 5 )}{2 x ^{2} - 5}

0 \leq x < \frac{5}{2} or x > \frac{5}{2}

Interval Notation

[0, \frac{5}{2}) \cup (\frac{5}{2}, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 0

Find undefined (singularity) points:

x = \frac{5}{2}, x = - \frac{5}{2}

Combine real regions and undefined points for final function domain

0 \leq x < \frac{5}{2} or x > \frac{5}{2}

f (x) = 5 x^{\frac{1}{3}} + 4

f (x) = \frac{3 x - 9}{- 2 x + 3}

f (x) = 3 x^{0.3}

f (x) = - \frac{1}{6} cos (6 x)

(0, 0), (4, 0)

What is the domain of (x+sqrt(x)(2x^2-5))/(2x^2-5) ?
The domain of (x+sqrt(x)(2x^2-5))/(2x^2-5) is 0<= x<sqrt(5/2)\lor x>sqrt(5/2)