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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

range

f (x) = 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

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

\frac{1 - 4 t}{6 + t}

\frac{2 x - 8}{x + 5}

f (x) = \frac{1}{x ^{2} + 6 x - 16}

x^{3} - 3

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