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

The range of sqrt((x-1)/(x+3)) is 0 1

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range of sqrt((x-1)/(x+3))

range

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

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 + 3} : x < - 3 or x \geq 1

Extreme Points of

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

Minimum

(1, 0)

Find the range for the interval

- \infty < x < - 3 : 1 < f (x) < \infty

Find the range for the interval

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

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

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

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

f (x) = x^{3} - 12 x^{2} + 36 x + 8

y = x + 9

- 2 sin (- 4 x + \frac{π}{2})

f (x) = 16 + 3 x

(12.7) (- 2.11)

What is the range of sqrt((x-1)/(x+3)) ?
The range of sqrt((x-1)/(x+3)) is 0<= f(x)<1\lor f(x)>1