What is the range of f(x)=sqrt(-2/3 (x-1/2))-3 ?

The range of f(x)=sqrt(-2/3 (x-1/2))-3 is f(x)>=-3

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range of f(x)=sqrt(-2/3 (x-1/2))-3

range

f (x) = - \frac{2}{3} (x - \frac{1}{2}) - 3

f (x) \geq - 3

Interval Notation

[- 3, \infty)

Solution steps

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

Domain of

- \frac{2}{3} (x - \frac{1}{2}) - 3 : x \leq \frac{1}{2}

Simplify

- \frac{2}{3} (x - \frac{1}{2}) - 3 : \frac{- 2 x + 1}{3} - 3

Extreme Points of

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

Minimum

(\frac{1}{2}, - 3)

Find the range for the interval

- \infty < x \leq \frac{1}{2} : - 3 \leq f (x) < \infty

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

f (x) \geq - 3

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

y = - 1 x + 2

(6, - 5), (2, 4)

y = \frac{1}{2} x

What is the range of f(x)=sqrt(-2/3 (x-1/2))-3 ?
The range of f(x)=sqrt(-2/3 (x-1/2))-3 is f(x)>=-3