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

The range of sqrt(x)+sqrt(1-x) is 1<= f(x)<= sqrt(2)

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

range

x + 1 - x

1 \leq f (x) \leq 2

Interval Notation

[1, 2]

Solution steps

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

Domain of

x + 1 - x : 0 \leq x \leq 1

Extreme Points of

x + 1 - x :

Minimum

(0, 1),

Maximum

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

Minimum

(1, 1)

Find the range for the interval

0 \leq x \leq 1 : 1 \leq f (x) \leq 2

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

1 \leq f (x) \leq 2

y = - 7 x + 8

f (x) = - \frac{1}{4} x - 2

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

f (x) = x^{2} - 6 x - 7

3 x + 5 y = 45, (- 5, 6)

What is the range of sqrt(x)+sqrt(1-x) ?
The range of sqrt(x)+sqrt(1-x) is 1<= f(x)<= sqrt(2)