What is the range of sqrt(x+4)+sqrt(5-x) ?

The range of sqrt(x+4)+sqrt(5-x) is 3<= f(x)<= 3sqrt(2)

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range of sqrt(x+4)+sqrt(5-x)

range

x + 4 + 5 - x

3 \leq f (x) \leq 32

Interval Notation

[3, 32]

Solution steps

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

Domain of

x + 4 + 5 - x : - 4 \leq x \leq 5

Extreme Points of

x + 4 + 5 - x :

Minimum

(- 4, 3),

Maximum

(\frac{1}{2}, 32),

Minimum

(5, 3)

Find the range for the interval

- 4 \leq x \leq 5 : 3 \leq f (x) \leq 32

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

3 \leq f (x) \leq 32

f (x) = \frac{6}{x - 2}

f (x) = 3^{x + 5} - 1

f (x) = \frac{2 x}{x ^{2} - 9}

f (x) = (x + 4)^{2} + 1

f (8) = 1 f (10) = - 2

What is the range of sqrt(x+4)+sqrt(5-x) ?
The range of sqrt(x+4)+sqrt(5-x) is 3<= f(x)<= 3sqrt(2)