What is the domain of f(x)=(sqrt(x-3))/(x^2+3x-40) ?

The domain of f(x)=(sqrt(x-3))/(x^2+3x-40) is 3 5

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domain of f(x)=(sqrt(x-3))/(x^2+3x-40)

domain

f (x) = \frac{x - 3}{x ^{2} + 3 x - 40}

3 \leq x < 5 or x > 5

Interval Notation

[3, 5) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 3

Find undefined (singularity) points:

x = 5, x = - 8

Combine real regions and undefined points for final function domain

3 \leq x < 5 or x > 5

What is the domain of f(x)=(sqrt(x-3))/(x^2+3x-40) ?
The domain of f(x)=(sqrt(x-3))/(x^2+3x-40) is 3<= x<5\lor x>5