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

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

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domain of f(x)=sqrt(1-(2x+3)/(x-1))

domain

f (x) = 1 - \frac{2 x + 3}{x - 1}

- 4 \leq x < 1

Interval Notation

[- 4, 1)

Solution steps

Find non-negative values for radicals:

- 4 \leq x < 1

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

- 4 \leq x < 1

f (x) = \frac{3}{x + 3}

f (x) = \frac{3}{2 x + 1}

f (x) = - 6 x^{2} - 9 x - 2

x^{3} - 15 x^{2} + 68 x - 96

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

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