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

The range of R(x)=3+cos(2x) is 2<= f(x)<= 4

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

range

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

2 \leq f (x) \leq 4

Solution steps

The range of the basic

cos

function is

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

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

Add to the edges of the range:

3

2 \leq cos (2 x) + 3 \leq 4

Therefore the range is

2 \leq f (x) \leq 4

f (x) = \frac{4 x - 24}{2 x - 4}

f (x) = \frac{x ^{2} - 4}{3 x ^{2}}

5.75 cos (\frac{π}{3} t) + 7.88

y = x^{4} - 4 x^{3} + 10

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

What is the range of R(x)=3+cos(2x) ?
The range of R(x)=3+cos(2x) is 2<= f(x)<= 4