What is the domain of 1/(5-x)+3sqrt(x-1) ?

The domain of 1/(5-x)+3sqrt(x-1) is 1 5

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domain of 1/(5-x)+3sqrt(x-1)

domain

\frac{1}{5 - x} + 3 x - 1

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

Combine real regions and undefined points for final function domain

1 \leq x < 5 or x > 5

sin (3 x)

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

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

f (x) = 2 cos (\frac{3 x}{2})

(- 1, 0), (7, 3)

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