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

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

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

domain

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

x \leq 2

Interval Notation

(- \infty, 2]

Solution steps

Find non-negative values for radicals:

x \leq 2

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x \leq 2

f (t) = 1 + 4 t - 3 t^{2}

f (x) = 2 x^{2} - 5 x + 6

f (x) = e^{x} - 8

f (x) = - \frac{15}{8}

f (x) = \frac{5 x + 5}{7 x + 21}

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