What is the range of f(x)=3cos(2x)+2 ?

The range of f(x)=3cos(2x)+2 is -1<= f(x)<= 5

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range of f(x)=3cos(2x)+2

range

f (x) = 3 cos (2 x) + 2

- 1 \leq f (x) \leq 5

Interval Notation

[- 1, 5]

Solution steps

The range of the basic

cos

function is

- 1 \leq cos (2 x) \leq 1

- 1 \leq cos (2 x) \leq 1

Multiply the edges of the range by:

3

- 3 \leq 3 cos (2 x) \leq 3

Add to the edges of the range:

2

- 1 \leq 3 cos (2 x) + 2 \leq 5

Therefore the range is

- 1 \leq f (x) \leq 5

What is the range of f(x)=3cos(2x)+2 ?
The range of f(x)=3cos(2x)+2 is -1<= f(x)<= 5