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intervalo (x^2)/(x^2+1)

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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range x²x²+1

Solution

0≤ f(x)<1

Interval Notation

[0, 1)

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Function range definition

The set of values of the dependent variable for which a function is defined

Rewrite as

x²x²+1 =y

Multiply both sides by x²+1

x²=y(x²+1)

The range is the set of y for which the discriminant is greater or equal to zero

Discriminant x²=y(x²+1): −4y²+4y

−4y²+4y≥ 0 : 0≤ y≤ 1

Check if the range interval endpoints are included

y=0 : Included

y=1 : Excluded

Therefore the range is

0≤ f(x)<1

Solve instead

domain x²x²+1

inverse x²x²+1

intercepts x²x²+1

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

intervalo (x^2)/(x^2+1)

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