What is the domain of f(x)= 1/(sqrt(x^2-7x+10)) ?

The domain of f(x)= 1/(sqrt(x^2-7x+10)) is x 5

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domain of f(x)= 1/(sqrt(x^2-7x+10))

domain

f (x) = \frac{1}{x ^{2} - 7 x + 10}

x < 2 or x > 5

Interval Notation

(- \infty, 2) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 2 or x \geq 5

Find undefined (singularity) points:

x = 5, x = 2

Combine real regions and undefined points for final function domain

x < 2 or x > 5

- 8 + 6 x - x^{2}

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

y = - \frac{2 x}{( x ^{2} - 25 ) ^{2}}

f (x) = \frac{- 1}{x ^{2} + 2 x - 24}

f (x) = 16 x - 5

What is the domain of f(x)= 1/(sqrt(x^2-7x+10)) ?
The domain of f(x)= 1/(sqrt(x^2-7x+10)) is x<2\lor x>5