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

The range of sqrt(x(x-2)) is f(x)>= 0

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range of sqrt(x(x-2))

range

x (x - 2)

f (x) \geq 0

Interval Notation

[0, \infty)

Solution steps

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

Domain of

x (x - 2) : x \leq 0 or x \geq 2

Extreme Points of

x (x - 2) :

Minimum

(0, 0),

Minimum

(2, 0)

Find the range for the interval

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

Find the range for the interval

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

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

f (x) \geq 0 or f (x) \geq 0

f (x) \geq 0

x + y = 1

f (x) = \frac{1}{2} (x + 6)

9 x^{2} - x^{3} + 2

(5.9) (9.6)

- y = 3 x + 3