What is the domain of f(x)=sqrt((-x^2+7x-10)/(x-3)) ?

The domain of f(x)=sqrt((-x^2+7x-10)/(x-3)) is x<= 2\lor 3<x<= 5

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domain of f(x)=sqrt((-x^2+7x-10)/(x-3))

domain

f (x) = \frac{- x ^{2} + 7 x - 10}{x - 3}

x \leq 2 or 3 < x \leq 5

Interval Notation

(- \infty, 2] \cup (3, 5]

Solution steps

Find non-negative values for radicals:

x \leq 2 or 3 < x \leq 5

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x \leq 2 or 3 < x \leq 5

g (x) = \frac{1}{x - 2}

\frac{sin ( x )}{cos ( x ) + 1}

f (x) = 4 t^{2} - 6

f (x) = \frac{1}{s - 3}

f (x) = \frac{( 1 - e ^{x} )}{ln ( x )}

What is the domain of f(x)=sqrt((-x^2+7x-10)/(x-3)) ?
The domain of f(x)=sqrt((-x^2+7x-10)/(x-3)) is x<= 2\lor 3<x<= 5