What is the domain of f(x)=(sqrt(x-1))/(x^2-16) ?

The domain of f(x)=(sqrt(x-1))/(x^2-16) is 1 4

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domain of f(x)=(sqrt(x-1))/(x^2-16)

domain

f (x) = \frac{x - 1}{x ^{2} - 16}

1 \leq x < 4 or x > 4

Interval Notation

[1, 4) \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 1

Find undefined (singularity) points:

x = 4, x = - 4

Combine real regions and undefined points for final function domain

1 \leq x < 4 or x > 4

f (x) = - 2 x^{2} - 2 x + 2

f (x) = 2 x + 3 y = 6

\frac{32}{y} - \frac{y + 1}{y + 7}

\frac{x - 3}{x - 4}

What is the domain of f(x)=(sqrt(x-1))/(x^2-16) ?
The domain of f(x)=(sqrt(x-1))/(x^2-16) is 1<= x<4\lor x>4