What is the domain of f(x)=sqrt(((x+1)(x-1))/x) ?

The domain of f(x)=sqrt(((x+1)(x-1))/x) is -1 = 1

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domain of f(x)=sqrt(((x+1)(x-1))/x)

domain

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

- 1 \leq x < 0 or x \geq 1

Interval Notation

[- 1, 0) \cup [1, \infty)

Solution steps

Find non-negative values for radicals:

- 1 \leq x < 0 or x \geq 1

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 1 \leq x < 0 or x \geq 1

(x + 2)^{2} (x - 1)

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

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

y = x^{3} + 3 x^{2} + 3 x + 2

y = \frac{1}{4} x

What is the domain of f(x)=sqrt(((x+1)(x-1))/x) ?
The domain of f(x)=sqrt(((x+1)(x-1))/x) is -1<= x<0\lor x>= 1