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

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

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

domain

f (x) = \frac{( 4 x + 3 )}{( 2 x - 1 )}

x \leq - \frac{3}{4} or x > \frac{1}{2}

Interval Notation

(- \infty, - \frac{3}{4}] \cup (\frac{1}{2}, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{3}{4} or x > \frac{1}{2}

Find undefined (singularity) points:

x = \frac{1}{2}

Combine real regions and undefined points for final function domain

x \leq - \frac{3}{4} or x > \frac{1}{2}

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

f (x) = \frac{2 x - 7}{3}

\frac{2}{3} x - 12

e^{2 x} - 3

f (x) = ∣ 8 + 6 x ∣

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