What is the domain of f(x)=ln(((9-x)/(2x+3))^{1/3}) ?

The domain of f(x)=ln(((9-x)/(2x+3))^{1/3}) is -3/2 <x<9

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domain of f(x)=ln(((9-x)/(2x+3))^{1/3})

domain

f (x) = ln ((\frac{9 - x}{2 x + 3})^{\frac{1}{3}})

- \frac{3}{2} < x < 9

Interval Notation

(- \frac{3}{2}, 9)

Solution steps

Find positive values for logs:

- \frac{3}{2} < x < 9

Find undefined (singularity) points:

x = - \frac{3}{2}

Combine real regions and undefined points for final function domain

- \frac{3}{2} < x < 9

f (x) = \frac{3 x ^{2}}{x ^{2} + 2 x - 35}

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

f (x) = 2 x + 1 + 4

lo g_{10} (x + 8)

What is the domain of f(x)=ln(((9-x)/(2x+3))^{1/3}) ?
The domain of f(x)=ln(((9-x)/(2x+3))^{1/3}) is -3/2 <x<9