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

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

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

domain

f (x) = \frac{3 x - 5}{4 - x}

\frac{5}{3} \leq x < 4

Interval Notation

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

Solution steps

Find non-negative values for radicals:

\frac{5}{3} \leq x < 4

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

\frac{5}{3} \leq x < 4

y = \frac{x ^{2}}{x ^{2} + 1}

2 x^{2} - 7

arcsin (2 cos (x))

\frac{4 - 11 x}{4 - 2 x}

g (x) = - lo g_{10} (2) (x + 4)

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