What is the domain of f(x)=sqrt((3-x)/(|2x-5|)) ?

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

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domain of f(x)=sqrt((3-x)/(|2x-5|))

domain

f (x) = \frac{3 - x}{∣ 2 x - 5 ∣}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = \frac{5}{2}

Combine real regions and undefined points for final function domain

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

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