What is the domain of f(x)=(sqrt(x-1))/(x^2+x-6) ?

The domain of f(x)=(sqrt(x-1))/(x^2+x-6) is 1 2

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domain of f(x)=(sqrt(x-1))/(x^2+x-6)

domain

f (x) = \frac{x - 1}{x ^{2} + x - 6}

1 \leq x < 2 or x > 2

Interval Notation

Solution steps

Find non-negative values for radicals:

x \geq 1

Find undefined (singularity) points:

x = 2, x = - 3

Combine real regions and undefined points for final function domain

1 \leq x < 2 or x > 2

y = \frac{x + 2}{x ^{2} - 9}

b^{y}

\frac{2 ( x + 3 ) ( x - 1 )}{( x - 1 ) ( x + 2 )}

\frac{x - 1}{x ^{2} + 3 x + 2}

g (x) = 2 x - 8 - 3

What is the domain of f(x)=(sqrt(x-1))/(x^2+x-6) ?
The domain of f(x)=(sqrt(x-1))/(x^2+x-6) is 1<= x<2\lor x>2