What is the range of sqrt((x+1)/(x-2)) ?

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

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range of sqrt((x+1)/(x-2))

range

\frac{x + 1}{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 + 1}{x - 2} : x \leq - 1 or x > 2

Extreme Points of

\frac{x + 1}{x - 2} :

None

Find the range for the interval

- \infty < x \leq - 1 : 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) = x^{2} + 4 x + 1

\frac{1 + 3 x ^{2} - x ^{3}}{x ^{2}}

y = 4 x - 9

f (x) = 3 x - 5

f (x) = - 6 x^{5} + 5 x^{3}

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