range of (x+1)/(x-1)

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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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Steps Examples

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range x+1x−1

Solution

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

Interval Notation

(−∞ , 1)∪(1, ∞ )

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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: x+1x−1

Inverse of x+1x−1 : 1+xx−1

1+xx−1

Find the domain of each inverse function

Domain of 1+xx−1 : x<1 or x>1

Combine the intervals

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

Solve instead

domain x+1x−1

inverse x+1x−1

intercepts x+1x−1

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