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範囲 a^4-a^2

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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range a⁴−a²

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: a⁴−a²

Inverse of a⁴−a²: √1+√1+4a2 , −√1+√1+4a2 , √1−√1+4a2 , −√1−√1+4a2

√1+√1+4a2 , −√1+√1+4a2 , √1−√1+4a2 , −√1−√1+4a2

Find the domain of each inverse function

Domain of √1+√1+4a2 : a≥ −14

Domain of −√1+√1+4a2 : a≥ −14

Domain of √1−√1+4a2 : −14 ≤ a≤ 0

Domain of −√1−√1+4a2 : −14 ≤ a≤ 0

Combine the intervals

f(x)≥ −14

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domain a⁴−a²

inverse a⁴−a²

intercepts a⁴−a²

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

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範囲 a^4-a^2

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範囲 a^4-a^2

Solution

Solution steps

Solve instead

Number Line

Graph