What is the domain of f(x)=sqrt((x^2-16)/(-x+3)) ?

The domain of f(x)=sqrt((x^2-16)/(-x+3)) is x<=-4\lor 3<x<= 4

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domain of f(x)=sqrt((x^2-16)/(-x+3))

domain

f (x) = \frac{x ^{2} - 16}{- x + 3}

x \leq - 4 or 3 < x \leq 4

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 4 or 3 < x \leq 4

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x \leq - 4 or 3 < x \leq 4

f (x) = - x^{2} + 10

g (x) = \frac{x + 9}{x ^{2} - 4}

y = 4 x^{2}

(3, - 5), (10, - 4)

What is the domain of f(x)=sqrt((x^2-16)/(-x+3)) ?
The domain of f(x)=sqrt((x^2-16)/(-x+3)) is x<=-4\lor 3<x<= 4