What is the domain of f(x)=sqrt((2x+3)/(1-5x)) ?

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

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domain of f(x)=sqrt((2x+3)/(1-5x))

domain

f (x) = \frac{2 x + 3}{1 - 5 x}

- \frac{3}{2} \leq x < \frac{1}{5}

Solution steps

Find non-negative values for radicals:

- \frac{3}{2} \leq x < \frac{1}{5}

Find undefined (singularity) points:

x = \frac{1}{5}

Combine real regions and undefined points for final function domain

- \frac{3}{2} \leq x < \frac{1}{5}

f (x) = \frac{x}{4 - x ^{2}}

f (x) = 7 x - 21

f (x) = 1 - 1

\frac{6 x}{7 x - 9}

4 x^{2} + 4 x + 1

What is the domain of f(x)=sqrt((2x+3)/(1-5x)) ?
The domain of f(x)=sqrt((2x+3)/(1-5x)) is -3/2 <= x< 1/5