What is the domain of sqrt((7x+1)/(4x-3)-2) ?

The domain of sqrt((7x+1)/(4x-3)-2) is 3/4 <x<= 7

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domain of sqrt((7x+1)/(4x-3)-2)

domain

\frac{7 x + 1}{4 x - 3} - 2

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

Interval Notation

(\frac{3}{4}, 7]

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = \frac{3}{4}

Combine real regions and undefined points for final function domain

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

y - 9 = \frac{7}{2} (x - 2)

f (x) = tanh (x)

(- 3, - 1), (9, 2)

x^{2} - 2 x + 5

x = 5

What is the domain of sqrt((7x+1)/(4x-3)-2) ?
The domain of sqrt((7x+1)/(4x-3)-2) is 3/4 <x<= 7