What is the domain of f(x)=ln(x/(sqrt(x+3))) ?

The domain of f(x)=ln(x/(sqrt(x+3))) is x>0

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domain of f(x)=ln(x/(sqrt(x+3)))

domain

f (x) = ln (\frac{x}{x + 3})

x > 0

Interval Notation

(0, \infty)

Solution steps

Find positive values for logs:

x > 0

Find undefined (singularity) points:

x = - 3

Combine real regions and undefined points for final function domain

x > 0

- x^{2} - 8 x

3 x^{2} - x - 2

\frac{2 + x}{3 - x}

3 e^{x^{2}}

f (x) = cos (x - \frac{π}{3})

What is the domain of f(x)=ln(x/(sqrt(x+3))) ?
The domain of f(x)=ln(x/(sqrt(x+3))) is x>0