What is the domain of f(x)=sqrt(((x-1))/(x^2-5x+6)) ?

The domain of f(x)=sqrt(((x-1))/(x^2-5x+6)) is 1 3

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domain of f(x)=sqrt(((x-1))/(x^2-5x+6))

domain

f (x) = \frac{( x - 1 )}{x ^{2} - 5 x + 6}

1 \leq x < 2 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

1 \leq x < 2 or x > 3

Find undefined (singularity) points:

x = 3, x = 2

Combine real regions and undefined points for final function domain

1 \leq x < 2 or x > 3

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

x^{2} y - x^{2} - 4 y = 0

\frac{4 x - 12}{( x - 2 ) ^{2}}

\frac{x}{- 2 x + 9}

What is the domain of f(x)=sqrt(((x-1))/(x^2-5x+6)) ?
The domain of f(x)=sqrt(((x-1))/(x^2-5x+6)) is 1<= x<2\lor x>3