What is the domain of f(x)=(3(x^2-2)^{1/2})/(1-x) ?

The domain of f(x)=(3(x^2-2)^{1/2})/(1-x) is x = 2^{1/2}

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domain of f(x)=(3(x^2-2)^{1/2})/(1-x)

domain

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

x \leq - 2^{\frac{1}{2}} or x \geq 2^{\frac{1}{2}}

Interval Notation

(- \infty, - 2^{\frac{1}{2}}] \cup [2^{\frac{1}{2}}, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 2^{\frac{1}{2}} or x \geq 2^{\frac{1}{2}}

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

x \leq - 2^{\frac{1}{2}} or x \geq 2^{\frac{1}{2}}

sin (2 x)

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

f (x) = \frac{ln ( x )}{x ^{2} - 5 x + 6}

\frac{x ^{2} - 4}{3 x - 1}

\frac{8 x}{7 x - 4}

What is the domain of f(x)=(3(x^2-2)^{1/2})/(1-x) ?
The domain of f(x)=(3(x^2-2)^{1/2})/(1-x) is x<=-2^{1/2}\lor x>= 2^{1/2}