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range of (2x^3+11x^2+5x)/(2x^2+x)

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

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range 2x³+11x²+5x2x²+x

Solution

f(x)<92 or 92 <f(x)<5 or f(x)>5

Interval Notation

(−∞ , 92 )∪(92 , 5)∪(5, ∞ )

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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 2x³+11x²+5x2x²+x : x<−12 or −12 <x<0 or x>0

Simplify 2x³+11x²+5x2x²+x : x+5

Extreme Points of x+5: None

Find the range for the interval −∞ <x<−12 : −∞ <f(x)<92

Find the range for the interval −12 <x<0: 92 <f(x)<5

Find the range for the interval 0<x<∞ : 5<f(x)<∞

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

f(x)<92 or 92 <f(x)<5 or f(x)>5

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domain 2x³+11x²+5x2x²+x

inverse 2x³+11x²+5x2x²+x

intercepts 2x³+11x²+5x2x²+x

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

range of (2x^3+11x^2+5x)/(2x^2+x)

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range of (2x^3+11x^2+5x)/(2x^2+x)

Solution

Solution steps

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