What is the domain of sqrt(1-(x+2)/(2x-1))+sqrt(5-x) ?

The domain of sqrt(1-(x+2)/(2x-1))+sqrt(5-x) is x< 1/2 \lor 3<= x<= 5

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domain of sqrt(1-(x+2)/(2x-1))+sqrt(5-x)

domain

1 - \frac{x + 2}{2 x - 1} + 5 - x

x < \frac{1}{2} or 3 \leq x \leq 5

Interval Notation

(- \infty, \frac{1}{2}) \cup [3, 5]

Solution steps

Find non-negative values for radicals:

x < \frac{1}{2} or 3 \leq x \leq 5

Find undefined (singularity) points:

x = \frac{1}{2}

Combine real regions and undefined points for final function domain

x < \frac{1}{2} or 3 \leq x \leq 5

f (x) = \frac{sin ( x )}{x - π}

f (x) = - 4 + 17 x - 19

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

f (x) = \frac{x - 1}{x ^{2} + 6 x - 16}

What is the domain of sqrt(1-(x+2)/(2x-1))+sqrt(5-x) ?
The domain of sqrt(1-(x+2)/(2x-1))+sqrt(5-x) is x< 1/2 \lor 3<= x<= 5