What is the domain of f(x)=(sqrt(-x^2+3x-2))/(x^2-4) ?

The domain of f(x)=(sqrt(-x^2+3x-2))/(x^2-4) is 1<= x<2

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domain of f(x)=(sqrt(-x^2+3x-2))/(x^2-4)

domain

f (x) = \frac{- x ^{2} + 3 x - 2}{x ^{2} - 4}

1 \leq x < 2

Interval Notation

[1, 2)

Solution steps

Find non-negative values for radicals:

1 \leq x \leq 2

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

1 \leq x < 2

f (x) = - 2 x + 2

\frac{4 x}{7 x - 8}

y = \frac{x ^{2}}{x - 1}

\frac{1}{x ( x ^{2} - 4 )}

f (x) = x x - 1

What is the domain of f(x)=(sqrt(-x^2+3x-2))/(x^2-4) ?
The domain of f(x)=(sqrt(-x^2+3x-2))/(x^2-4) is 1<= x<2