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

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

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

domain

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

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

Interval Notation

[- \frac{3}{4}, 2)

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

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

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

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

x^{2} + 8 x

f (x) = \frac{3}{cos ( x ) - 1} + 10

f (x) = \frac{1}{4 - t ^{2}}

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