What is the domain of f(x)=(sqrt(x-1))/(3x^2-75) ?

The domain of f(x)=(sqrt(x-1))/(3x^2-75) is 1 5

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domain of f(x)=(sqrt(x-1))/(3x^2-75)

domain

f (x) = \frac{x - 1}{3 x ^{2} - 75}

1 \leq x < 5 or x > 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq 1

Find undefined (singularity) points:

x = 5, x = - 5

Combine real regions and undefined points for final function domain

1 \leq x < 5 or x > 5

What is the domain of f(x)=(sqrt(x-1))/(3x^2-75) ?
The domain of f(x)=(sqrt(x-1))/(3x^2-75) is 1<= x<5\lor x>5