What is the range of 3+cos(2t) ?

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

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range of 3+cos(2t)

range

3 + cos (2 t)

2 \leq f (t) \leq 4

Interval Notation

[2, 4]

Solution steps

The range of the basic

cos

function is

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

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

Add to the edges of the range:

3

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

Therefore the range is

2 \leq f (t) \leq 4

f (x) = \frac{x - 7}{x ^{2} - 49}

x^{2} + 2 x + 12

16 - x^{2}

f (x) = \frac{x - 2}{x ^{2} - 4} + \frac{1}{x}

\frac{2}{3}