What is the domain of sqrt((-3x+7)/(x-1)) ?

The domain of sqrt((-3x+7)/(x-1)) is 1<x<= 7/3

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domain of sqrt((-3x+7)/(x-1))

domain

\frac{- 3 x + 7}{x - 1}

1 < x \leq \frac{7}{3}

Interval Notation

(1, \frac{7}{3}]

Solution steps

Find non-negative values for radicals:

1 < x \leq \frac{7}{3}

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

1 < x \leq \frac{7}{3}

f (x) = 5 - x (5 x^{2} + 4)

f (x) = ∣ 3 x - 9 ∣

1 - x^{2} + 5

f (x) = \frac{x - 7}{x ^{2} - 14 x + 49}

h (x) = 5 - x

What is the domain of sqrt((-3x+7)/(x-1)) ?
The domain of sqrt((-3x+7)/(x-1)) is 1<x<= 7/3