What is the range of 2-3cos(2x) ?

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

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range of 2-3cos(2x)

range

2 - 3 cos (2 x)

- 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

x^{2} + 36 y^{2} = 36

6 sin (3 x - π)

f (x) = \frac{1}{x ^{3}}

ln (\frac{1}{1 + e ^{- x}})

f (x) = (x + 7)^{3} - 2