What is the domain of y=-sqrt((4x-3)/(x-1)) ?

The domain of y=-sqrt((4x-3)/(x-1)) is x 1

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domain of y=-sqrt((4x-3)/(x-1))

domain

x \leq \frac{3}{4} or x > 1

Interval Notation

(- \infty, \frac{3}{4}] \cup (1, \infty)

Solution steps

Find non-negative values for radicals:

x \leq \frac{3}{4} or x > 1

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

x \leq \frac{3}{4} or x > 1

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