What is the domain of f(x)=sqrt(3-2*1/(x-2)) ?

The domain of f(x)=sqrt(3-2*1/(x-2)) is x = 8/3

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domain of f(x)=sqrt(3-2*1/(x-2))

domain

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

x < 2 or x \geq \frac{8}{3}

Interval Notation

Solution steps

Find non-negative values for radicals:

x < 2 or x \geq \frac{8}{3}

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x < 2 or x \geq \frac{8}{3}

f (t) = 4 - 2 t

\frac{x}{x ^{2} - 5 x - 6}

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

f (x) = x - 5 x^{3} - x^{2} - 2 x

f (x) = lo g_{3} (3 x - 6)

What is the domain of f(x)=sqrt(3-2*1/(x-2)) ?
The domain of f(x)=sqrt(3-2*1/(x-2)) is x<2\lor x>= 8/3