What is the domain of f(x)=(sqrt((13-2x)))/(x-4) ?

The domain of f(x)=(sqrt((13-2x)))/(x-4) is x<4\lor 4<x<= 13/2

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domain of f(x)=(sqrt((13-2x)))/(x-4)

domain

f (x) = \frac{( 13 - 2 x )}{x - 4}

x < 4 or 4 < x \leq \frac{13}{2}

Interval Notation

(- \infty, 4) \cup (4, \frac{13}{2}]

Solution steps

Find non-negative values for radicals:

x \leq \frac{13}{2}

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x < 4 or 4 < x \leq \frac{13}{2}

What is the domain of f(x)=(sqrt((13-2x)))/(x-4) ?
The domain of f(x)=(sqrt((13-2x)))/(x-4) is x<4\lor 4<x<= 13/2