What is the domain of f(x)=(sqrt(x-1))/(x-4) ?

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

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domain of f(x)=(sqrt(x-1))/(x-4)

domain

f (x) = \frac{x - 1}{x - 4}

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

Combine real regions and undefined points for final function domain

1 \leq x < 4 or x > 4

f (x) = \frac{1}{2} e^{x + 3} - 4

f (x) = 3 x (x + 3) (x - 5)

2 sin (\frac{2 π θ}{3})

f (x) = \frac{x ^{2} - 25}{x - 5}

2 + ln (x)

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