What is the range of 2sin(2x)+3 ?

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

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range of 2sin(2x)+3

range

2 sin (2 x) + 3

1 \leq f (x) \leq 5

Interval Notation

[1, 5]

Solution steps

The range of the basic

sin

function is

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

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

Multiply the edges of the range by:

2

- 2 \leq 2 sin (2 x) \leq 2

Add to the edges of the range:

3

1 \leq 2 sin (2 x) + 3 \leq 5

Therefore the range is

1 \leq f (x) \leq 5

cot (3 x^{2})

f (x) = 3 x + 12

\frac{x + 2}{x - 1}

f (x) = \frac{5}{x + 7} + 3

(8, - 3), (4, - 7)