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

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

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

domain

y = \frac{x - 1}{x - 4}

x \leq 1 or x > 4

Interval Notation

Solution steps

Find non-negative values for radicals:

x \leq 1 or x > 4

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x \leq 1 or x > 4

f (x) = - - 2 x + 5

\frac{x + 7}{x + 11}

f (x) = \frac{x + 6}{x ^{2} + 2 x - 24}

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

\frac{7 x + 6}{x - 5}

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