What is the domain of f(x)=ln((5-x)/(3+x)) ?

The domain of f(x)=ln((5-x)/(3+x)) is -3<x<5

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domain of f(x)=ln((5-x)/(3+x))

domain

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

- 3 < x < 5

Interval Notation

(- 3, 5)

Solution steps

Find positive values for logs:

- 3 < x < 5

Find undefined (singularity) points:

x = - 3

Combine real regions and undefined points for final function domain

- 3 < x < 5

\frac{9 x ^{2} - 8 x - 7}{( x + 3 ) ( 4 x - 2 )}

9 - 8 x

f (x) = \frac{x ( x + 2 )}{3 ( x - 7 )}

f (x) = arccsch (x)

y = lo g_{3} (x^{2} - 4)

What is the domain of f(x)=ln((5-x)/(3+x)) ?
The domain of f(x)=ln((5-x)/(3+x)) is -3<x<5