What is the range of y=sqrt((x+5)/(x-2)) ?

The range of y=sqrt((x+5)/(x-2)) is 0 1

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range of y=sqrt((x+5)/(x-2))

range

y = \frac{x + 5}{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 + 5}{x - 2} : x \leq - 5 or x > 2

Extreme Points of

\frac{x + 5}{x - 2} :

None

Find the range for the interval

- \infty < x \leq - 5 : 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) = \frac{( 1 + 9 x )}{4 - 4 x}

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

f (x) = \frac{4 ^{x}}{1 + 4 ^{x}}

f (x) = x^{3} - x^{2} - x + 9

What is the range of y=sqrt((x+5)/(x-2)) ?
The range of y=sqrt((x+5)/(x-2)) is 0<= f(x)<1\lor f(x)>1