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}

Interval Notation

[1, \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}

y = \frac{x - 2}{x + 2}

\frac{∣ x - 2 ∣ - 1}{[ x + 3 ] + 2}

y = \frac{x + 6}{15 - x ^{2} - 64}

(x + 3) 2 - 2

7 x^{2} - 10 x + 5

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