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critical points of 3x^2y+y^3-3x^2-3y^2+2

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

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

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range (7x²+6)(2x²−4)

Solution

f(x)≥ −2007

Interval Notation

[−2007 , ∞ )

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Function range definition

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

The function range is the combined domain of the inverse functions

Find the inverse function(s) of: (7x²+6)(2x²−4)

Inverse of (7x²+6)(2x²−4): √7√16+√56x+160014 , −√7√16+√56x+160014 , √7√16−√56x+160014 , −√7√16−√56x+160014

√7√16+√56x+160014 , −√7√16+√56x+160014 , √7√16−√56x+160014 , −√7√16−√56x+160014

Find the domain of each inverse function

Domain of √7√16+√56x+160014 : x≥ −2007

Domain of −√7√16+√56x+160014 : x≥ −2007

Domain of √7√16−√56x+160014 : −2007 ≤ x≤ −24

Domain of −√7√16−√56x+160014 : −2007 ≤ x≤ −24

Combine the intervals

f(x)≥ −2007

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domain (7x²+6)(2x²−4)

inverse (7x²+6)(2x²−4)

intercepts (7x²+6)(2x²−4)

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

critical points of 3x^2y+y^3-3x^2-3y^2+2

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