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range of (x^2+4x-45)/(x^2+x-30)

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

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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 x²+4x−45x²+x−30

Solution

f(x)<1 or 1<f(x)<1411 or f(x)>1411

Interval Notation

(−∞ , 1)∪(1, 1411 )∪(1411 , ∞ )

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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 x²+4x−45x²+x−30 : x<−6 or −6<x<5 or x>5

Simplify x²+4x−45x²+x−30 : x+9x+6

Extreme Points of x+9x+6 : None

Find the range for the interval −∞ <x<−6: −∞ <f(x)<1

Find the range for the interval −6<x<5: 1411 <f(x)<∞

Find the range for the interval 5<x<∞ : 1<f(x)<1411

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

f(x)<1 or f(x)>1411 or 1<f(x)<1411

f(x)<1 or 1<f(x)<1411 or f(x)>1411

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domain x²+4x−45x²+x−30

inverse x²+4x−45x²+x−30

intercepts x²+4x−45x²+x−30

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

range of (x^2+4x-45)/(x^2+x-30)

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