What is the range of 2cos(x)+1 ?

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

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range of 2cos(x)+1

range

2 cos (x) + 1

- 1 \leq f (x) \leq 3

Interval Notation

[- 1, 3]

Solution steps

The range of the basic

cos

function is

- 1 \leq cos (x) \leq 1

- 1 \leq cos (x) \leq 1

Multiply the edges of the range by:

2

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

Add to the edges of the range:

1

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

Therefore the range is

- 1 \leq f (x) \leq 3

y = 1

f (x) = 2 x^{2} - 4 x - 5

\frac{9}{x + 2}

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

y = \frac{3}{2} x + 2