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range of 3cos(2x+pi/4)+1

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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√☐

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log_□

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∞

∫

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≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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range 3cos(2x+π4 )+1

Solution

−2≤ f(x)≤ 4

Interval Notation

[−2, 4]

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Solution steps

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Function range definition

The set of values of the dependent variable for which a function is defined

The range of the basic cos function is −1≤ cos(2x+π4 )≤ 1

−1≤ cos(2x+π4 )≤ 1

Multiply the edges of the range by: 3

−3≤ 3cos(2x+π4 )≤ 3

Add to the edges of the range: 1

−2≤ 3cos(2x+π4 )+1≤ 4

Therefore the range is

−2≤ f(x)≤ 4

Solve instead

domain 3cos(2x+π4 )+1

periodicity 3cos(2x+π4 )+1

amplitude 3cos(2x+π4 )+1

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

range of 3cos(2x+pi/4)+1

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