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range of (\frac{2x-2)/(6x)}{(4x)/(x-1)}

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

☐²

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ddx

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

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range 2x−26x 4xx−1

Solution

f(x)>0

Interval Notation

(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

Find the minimum and maximum value in each defined interval and unite the results

Domain of 2x−26x 4xx−1 : x<0 or 0<x<1 or x>1

Simplify 2x−26x 4xx−1 : (x−1)²12x²

Extreme Points of (x−1)²12x² : Minimum(1, 0)

Find the range for the interval −∞ <x<0: 112 <f(x)<∞

Find the range for the interval 0<x<1: 0<f(x)<∞

Find the range for the interval 1<x<∞ : 0<f(x)<112

Combine the ranges of all domain intervals to obtain the function range

f(x)>112 or f(x)>0 or 0<f(x)<112

f(x)>0

Solve instead

domain 2x−26x 4xx−1

inverse 2x−26x 4xx−1

intercepts 2x−26x 4xx−1

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

range of (\frac{2x-2)/(6x)}{(4x)/(x-1)}

Solution

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