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

f (x) = \frac{x ^{2} - 5 x + 4}{3 - x}

x \leq 1 or 3 < x \leq 4

Interval Notation

(- \infty, 1] \cup (3, 4]

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

f (x) = - x^{2} + 11

25 - x^{2}

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

f (x) = \frac{1}{x ^{6}}

8 x^{3} + 3 x

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