What is the domain of f(x)=sqrt((x-8)/(x-2)+6) ?

The domain of f(x)=sqrt((x-8)/(x-2)+6) is x = 20/7

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domain of f(x)=sqrt((x-8)/(x-2)+6)

domain

f (x) = \frac{x - 8}{x - 2} + 6

x < 2 or x \geq \frac{20}{7}

Interval Notation

(- \infty, 2) \cup [\frac{20}{7}, \infty)

Solution steps

Find non-negative values for radicals:

x < 2 or x \geq \frac{20}{7}

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x < 2 or x \geq \frac{20}{7}

x^{3} + 2 x^{2} - 16 x - 32

(- 1, 3), (2, - 4)

\frac{2}{x - 6}

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

f (x) = \frac{4 x - 7}{x - 3}

What is the domain of f(x)=sqrt((x-8)/(x-2)+6) ?
The domain of f(x)=sqrt((x-8)/(x-2)+6) is x<2\lor x>= 20/7