What is the domain of f(x)=(sqrt(2-7x))/(x-4) ?

The domain of f(x)=(sqrt(2-7x))/(x-4) is x<= 2/7

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domain of f(x)=(sqrt(2-7x))/(x-4)

domain

f (x) = \frac{2 - 7 x}{x - 4}

x \leq \frac{2}{7}

Interval Notation

(- \infty, \frac{2}{7}]

Solution steps

Find non-negative values for radicals:

x \leq \frac{2}{7}

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x \leq \frac{2}{7}

What is the domain of f(x)=(sqrt(2-7x))/(x-4) ?
The domain of f(x)=(sqrt(2-7x))/(x-4) is x<= 2/7