What is the domain of f(x)=(sqrt(3y+2))/(sqrt(4-5y)) ?

The domain of f(x)=(sqrt(3y+2))/(sqrt(4-5y)) is -2/3 <= y< 4/5

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domain of f(x)=(sqrt(3y+2))/(sqrt(4-5y))

domain

- \frac{2}{3} \leq y < \frac{4}{5}

Interval Notation

[- \frac{2}{3}, \frac{4}{5})

Solution steps

Find non-negative values for radicals:

- \frac{2}{3} \leq y \leq \frac{4}{5}

Find undefined (singularity) points:

y = \frac{4}{5}

Combine real regions and undefined points for final function domain

- \frac{2}{3} \leq y < \frac{4}{5}

What is the domain of f(x)=(sqrt(3y+2))/(sqrt(4-5y)) ?
The domain of f(x)=(sqrt(3y+2))/(sqrt(4-5y)) is -2/3 <= y< 4/5