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domain of sqrt(6x)

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

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range 20(x−3)(x+4)(x−3)²(x−5)

Solution

f(x)≤ −30√7−80 or 30√7−80≤ f(x)<0 or f(x)>0

Interval Notation

(−∞ , −30√7−80]∪ [30√7−80, 0)∪(0, ∞ )

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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 function range is the combined domain of the inverse functions

Find the inverse function(s) of: 20(x−3)(x+4)(x−3)²(x−5)

Inverse of 20(x−3)(x+4)(x−3)²(x−5) : 4x+10+√x²+160x+100x , 4x+10−√x²+160x+100x

4x+10+√x²+160x+100x , 4x+10−√x²+160x+100x

Find the domain of each inverse function

Domain of 4x+10+√x²+160x+100x : x≤ −30√7−80 or 30√7−80≤ x<0 or x>0

Domain of 4x+10−√x²+160x+100x : x≤ −30√7−80 or 30√7−80≤ x<0 or x>0

Combine the intervals

f(x)≤ −30√7−80 or 30√7−80≤ f(x)<0 or f(x)>0

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domain 20(x−3)(x+4)(x−3)²(x−5)

inverse 20(x−3)(x+4)(x−3)²(x−5)

intercepts 20(x−3)(x+4)(x−3)²(x−5)

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

domain of sqrt(6x)

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