What is the domain of f(x)=((1))/(\sqrt[4]{2x^2-1)} ?

The domain of f(x)=((1))/(\sqrt[4]{2x^2-1)} is x 1/(sqrt(2))

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domain of f(x)=((1))/(\sqrt[4]{2x^2-1)}

domain

x < - \frac{1}{2} or x > \frac{1}{2}

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = \frac{1}{2}, x = - \frac{1}{2}

Combine real regions and undefined points for final function domain

x < - \frac{1}{2} or x > \frac{1}{2}

y = \frac{( x ^{3} )}{x ^{2} - 9}

f (x) = - 3 x + 9

x + 3 y = 0

f (x) = 4 x^{2} - 24 x + 31

(7, 8), (- 7, 1)

What is the domain of f(x)=((1))/(\sqrt[4]{2x^2-1)} ?
The domain of f(x)=((1))/(\sqrt[4]{2x^2-1)} is x<-1/(sqrt(2))\lor x> 1/(sqrt(2))