What is the range of sqrt(x/(x-2)) ?

The range of sqrt(x/(x-2)) is 0 1

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range of sqrt(x/(x-2))

range

\frac{x}{x - 2}

0 \leq f (x) < 1 or f (x) > 1

Interval Notation

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

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

\frac{x}{x - 2} : x \leq 0 or x > 2

Extreme Points of

\frac{x}{x - 2} :

None

Find the range for the interval

- \infty < x \leq 0 : 0 \leq f (x) < 1

Find the range for the interval

2 < x < \infty : 1 < f (x) < \infty

Combine the ranges of all domain intervals to obtain the function range

0 \leq f (x) < 1 or f (x) > 1

0 \leq f (x) < 1 or f (x) > 1

f (x) = - 4 x + \frac{2}{x}

x^{2} - 3 x

f (x) = - \frac{7}{5} x - 4

f (x) = - x^{2} - 6 x

- 3 csc (2 π x)

What is the range of sqrt(x/(x-2)) ?
The range of sqrt(x/(x-2)) is 0<= f(x)<1\lor f(x)>1