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

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

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

domain

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

x \leq - 5 - 1 or x \geq 5 - 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 5 - 1 or x \geq 5 - 1

The function domain

x \leq - 5 - 1 or x \geq 5 - 1

8 + x

f (x) = 5 x 4 x - x^{2}

\frac{x}{x - 4}

\frac{x}{x - 8}

\frac{6 x}{x ^{2} - 2 x}

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