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

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

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

domain

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

x \leq - 4 or 0 < x < 3 or x \geq 4

Interval Notation

(- \infty, - 4] \cup (0, 3) \cup [4, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 4 or 0 < x < 3 or x \geq 4

Find undefined (singularity) points:

x = 3, x = 0

Combine real regions and undefined points for final function domain

x \leq - 4 or 0 < x < 3 or x \geq 4

f (x) = sin (x) + x

f (x) = lo g_{10} (2 x - 200)

f (x) = x^{3} - 5 x^{2} + 6 x

\frac{25 - e ^{x^{2}}}{1 - e ^{25 - x^{2}}}

f (x) = \frac{x - 7}{x ^{2}}

What is the domain of f(x)=sqrt((x^2-16)/(x^2-3x)) ?
The domain of f(x)=sqrt((x^2-16)/(x^2-3x)) is x<=-4\lor 0<x<3\lor x>= 4