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

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

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

domain

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

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = \frac{3}{2}

Combine real regions and undefined points for final function domain

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

f (x) = 3 x^{2} - 5 x - 2

f (x) = 2 ∣ x ∣

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

f (x) = (100 - x^{2})^{\frac{5}{2}}

\frac{x}{x ^{2} + 64}

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