What is the range of f(x)=sin(x)+cos(x) ?

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

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range of f(x)=sin(x)+cos(x)

range

f (x) = sin (x) + cos (x)

- 2 \leq f (x) \leq 2

Interval Notation

[- 2, 2]

Solution steps

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

Domain of

sin (x) + cos (x) : - \infty < x < \infty

Extreme Points of

sin (x) + cos (x) :

Maximum

(\frac{π}{4} + 2 πn, 2),

Minimum

(\frac{5 π}{4} + 2 πn, - 2)

Find the range for the interval

- \infty < x < \infty : - 2 \leq f (x) \leq 2

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

- 2 \leq f (x) \leq 2

f (x) = - 2 x + 4

x^{3} - 7

25 - x^{2} \cdot x + 3

f (x) = (x^{2} + 5 x)

f (x) = 2 x^{2} - 5 x - 3

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