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sin^2(45^{\circ})+cos^2(30^{\circ})

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range x⁴−x²

Solution

f(x)≥ −14

Interval Notation

[−14 , ∞ )

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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: x⁴−x²

Inverse of x⁴−x²: √1+√1+4x2 , −√1+√1+4x2 , √1−√1+4x2 , −√1−√1+4x2

√1+√1+4x2 , −√1+√1+4x2 , √1−√1+4x2 , −√1−√1+4x2

Find the domain of each inverse function

Domain of √1+√1+4x2 : x≥ −14

Domain of −√1+√1+4x2 : x≥ −14

Domain of √1−√1+4x2 : −14 ≤ x≤ 0

Domain of −√1−√1+4x2 : −14 ≤ x≤ 0

Combine the intervals

f(x)≥ −14

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domain x⁴−x²

inverse x⁴−x²

intercepts x⁴−x²

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

sin^2(45^{\circ})+cos^2(30^{\circ})

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sin^2(45^{\circ})+cos^2(30^{\circ})

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