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range of -5x+e^x

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

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

simplify solve for expand factor rationalize

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range (x²+1)(x²−1)

Solution

f(x)≥ −1

Interval Notation

[−1, ∞ )

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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: (x²+1)(x²−1)

Inverse of (x²+1)(x²−1): ⁴√x+1, −⁴√x+1

⁴√x+1, −⁴√x+1

Find the domain of each inverse function

Domain of ⁴√x+1 : x≥ −1

Domain of −⁴√x+1 : x≥ −1

Combine the intervals

f(x)≥ −1

Solve instead

domain (x²+1)(x²−1)

inverse (x²+1)(x²−1)

intercepts (x²+1)(x²−1)

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

range of -5x+e^x

Solution

Solution steps

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