What is the domain of f(x)=sqrt((x^2-5x+4)/(3-x)) ?

The domain of f(x)=sqrt((x^2-5x+4)/(3-x)) is x<= 1\lor 3<x<= 4

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domain of f(x)=sqrt((x^2-5x+4)/(3-x))

domain

x \leq 1 or 3 < x \leq 4

Interval Notation

Solution steps

Find non-negative values for radicals:

x \leq 1 or 3 < x \leq 4

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x \leq 1 or 3 < x \leq 4

What is the domain of f(x)=sqrt((x^2-5x+4)/(3-x)) ?
The domain of f(x)=sqrt((x^2-5x+4)/(3-x)) is x<= 1\lor 3<x<= 4