What is the range of-2sin(x/2-pi/3)+5 ?

The range of-2sin(x/2-pi/3)+5 is 3<= f(x)<= 7

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range of-2sin(x/2-pi/3)+5

range

- 2 sin (\frac{x}{2} - \frac{π}{3}) + 5

3 \leq f (x) \leq 7

Interval Notation

[3, 7]

Solution steps

The range of the basic

sin

function is

- 1 \leq sin (\frac{x}{2} - \frac{π}{3}) \leq 1

- 1 \leq sin (\frac{x}{2} - \frac{π}{3}) \leq 1

Multiply the edges of the range by:

- 2

- 2 \leq - 2 sin (\frac{x}{2} - \frac{π}{3}) \leq 2

Add to the edges of the range:

5

3 \leq - 2 sin (\frac{x}{2} - \frac{π}{3}) + 5 \leq 7

Therefore the range is

3 \leq f (x) \leq 7

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

f (x) = \frac{x - 4}{3 x + 5}

cos (4 x)

f (x) = 4 - 5 x

- 16 t^{2} + 1700

What is the range of-2sin(x/2-pi/3)+5 ?
The range of-2sin(x/2-pi/3)+5 is 3<= f(x)<= 7