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

The domain of f(x)=sqrt(1-1/(x^2+2x-3)) is x =-1+sqrt(5)

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domain of f(x)=sqrt(1-1/(x^2+2x-3))

domain

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

x \leq - 1 - 5 or - 3 < x < 1 or x \geq - 1 + 5

Interval Notation

(- \infty, - 1 - 5] \cup (- 3, 1) \cup [- 1 + 5, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 1 - 5 or - 3 < x < 1 or x \geq - 1 + 5

Find undefined (singularity) points:

x = 1, x = - 3

Combine real regions and undefined points for final function domain

x \leq - 1 - 5 or - 3 < x < 1 or x \geq - 1 + 5

3 + x

f (x) = lo g_{2} (2^{x})

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

f (x) = \frac{5 x}{3 x ( x + 12 )}

f (x) = e^{6 x - 5}

What is the domain of f(x)=sqrt(1-1/(x^2+2x-3)) ?
The domain of f(x)=sqrt(1-1/(x^2+2x-3)) is x<=-1-sqrt(5)\lor-3<x<1\lor x>=-1+sqrt(5)