What is the domain of f(x)=(sqrt((11-2x)))/(x-3) ?

The domain of f(x)=(sqrt((11-2x)))/(x-3) is x<3\lor 3<x<= 11/2

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domain of f(x)=(sqrt((11-2x)))/(x-3)

domain

f (x) = \frac{( 11 - 2 x )}{x - 3}

x < 3 or 3 < x \leq \frac{11}{2}

Interval Notation

(- \infty, 3) \cup (3, \frac{11}{2}]

Solution steps

Find non-negative values for radicals:

x \leq \frac{11}{2}

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x < 3 or 3 < x \leq \frac{11}{2}

\frac{6 - 3 x}{x - 10}

4 cos (\frac{x}{2})

x - y = - 2

f (x) = x^{4} - 2 x^{2} + 3

f (x) = x + 2 sin (x)

What is the domain of f(x)=(sqrt((11-2x)))/(x-3) ?
The domain of f(x)=(sqrt((11-2x)))/(x-3) is x<3\lor 3<x<= 11/2