What is the range of sqrt(-x^2-13x-12) ?

The range of sqrt(-x^2-13x-12) is 0<= f(x)<= 11/2

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range of sqrt(-x^2-13x-12)

range

- x^{2} - 13 x - 12

0 \leq f (x) \leq \frac{11}{2}

Interval Notation

[0, \frac{11}{2}]

Solution steps

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

Domain of

- x^{2} - 13 x - 12 : - 12 \leq x \leq - 1

Extreme Points of

- x^{2} - 13 x - 12 :

Minimum

(- 12, 0),

Maximum

(- \frac{13}{2}, \frac{11}{2}),

Minimum

(- 1, 0)

Find the range for the interval

- 12 \leq x \leq - 1 : 0 \leq f (x) \leq \frac{11}{2}

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

0 \leq f (x) \leq \frac{11}{2}

(0, 2), (3, 1)

f (x) = 2 x^{4} - 12 x^{2}

f (x) = \frac{3}{5} x^{3} - 7 x + 4

x + 6

\frac{1}{x - 2} - 4

What is the range of sqrt(-x^2-13x-12) ?
The range of sqrt(-x^2-13x-12) is 0<= f(x)<= 11/2