What is the domain of f(x)=sqrt(((3x-4))/((7-2x))) ?

The domain of f(x)=sqrt(((3x-4))/((7-2x))) is 4/3 <= x< 7/2

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domain of f(x)=sqrt(((3x-4))/((7-2x)))

domain

f (x) = \frac{( 3 x - 4 )}{( 7 - 2 x )}

\frac{4}{3} \leq x < \frac{7}{2}

Interval Notation

Solution steps

Find non-negative values for radicals:

\frac{4}{3} \leq x < \frac{7}{2}

Find undefined (singularity) points:

x = \frac{7}{2}

Combine real regions and undefined points for final function domain

\frac{4}{3} \leq x < \frac{7}{2}

\frac{3}{t - 1}

\frac{\frac{1}{x - 4}}{3 - \frac{1}{x - 4}}

f (x) = \frac{1}{t + 2}

f (x) = 2 x^{2} - 4 x - 16

f (x) = 6 + x^{2}

What is the domain of f(x)=sqrt(((3x-4))/((7-2x))) ?
The domain of f(x)=sqrt(((3x-4))/((7-2x))) is 4/3 <= x< 7/2