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

The domain of f(x)=(sqrt(t-2))/(2t-6) is 2 3

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

domain

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

2 \leq t < 3 or t > 3

Interval Notation

[2, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

t \geq 2

Find undefined (singularity) points:

t = 3

Combine real regions and undefined points for final function domain

2 \leq t < 3 or t > 3

What is the domain of f(x)=(sqrt(t-2))/(2t-6) ?
The domain of f(x)=(sqrt(t-2))/(2t-6) is 2<= t<3\lor t>3