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

The domain of f(x)=(4x)/(sqrt(2x)-3) is 0 9/2

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

domain

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

0 \leq x < \frac{9}{2} or x > \frac{9}{2}

Interval Notation

Solution steps

Find non-negative values for radicals:

x \geq 0

Find undefined (singularity) points:

x = \frac{9}{2}

Combine real regions and undefined points for final function domain

0 \leq x < \frac{9}{2} or x > \frac{9}{2}

0

\frac{- ( x + 1 )}{2}

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

lo g_{10} (x + 4)

f (x) = \frac{9 - x}{x - 7}

What is the domain of f(x)=(4x)/(sqrt(2x)-3) ?
The domain of f(x)=(4x)/(sqrt(2x)-3) is 0<= x< 9/2 \lor x> 9/2