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

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

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

domain

f (x) = 1 + \frac{3 - x}{5 - x}

x \leq 3 or x > 5

Interval Notation

(- \infty, 3] \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 3 or x > 5

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

x \leq 3 or x > 5

f (x) = \frac{x + 5}{x ^{2} - 10 x + 25}

sec (x)

- 9

x^{3} - 17 x^{2} + 48 x - 32

\frac{2}{3} cos (2 (\frac{θ}{3} - π)) + \frac{1}{2}

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