What is the domain of f(x)=(sqrt(2x^2-6))/(x-4) ?

The domain of f(x)=(sqrt(2x^2-6))/(x-4) is x 4

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domain of f(x)=(sqrt(2x^2-6))/(x-4)

domain

f (x) = \frac{2 x ^{2} - 6}{x - 4}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 3 or x \geq 3

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

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

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

y = \frac{2 x + 3}{x - 1}

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

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

f (x) = \frac{2 x + 3}{1 - 5 x}

What is the domain of f(x)=(sqrt(2x^2-6))/(x-4) ?
The domain of f(x)=(sqrt(2x^2-6))/(x-4) is x<=-sqrt(3)\lor sqrt(3)<= x<4\lor x>4