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

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

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

domain

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

x \leq - 1 or 4 \leq x < 5

Interval Notation

(- \infty, - 1] \cup [4, 5)

Solution steps

Find non-negative values for radicals:

x \leq - 1 or 4 \leq x < 5

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

x \leq - 1 or 4 \leq x < 5

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