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

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

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

domain

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

- 2 \leq x \leq 2 or x > 4

Interval Notation

[- 2, 2] \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

- 2 \leq x \leq 2 or x > 4

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

- 2 \leq x \leq 2 or x > 4

f (x) = 1 + 6 sec^{2} (\frac{x}{5})

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

f (x) = \frac{( x - 3 )}{( x - 7 )}

x^{\frac{1}{3}}

f (x) = 2 + \frac{1 + x}{9 - x ^{2}}

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