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inversa 2^{x-3}

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

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range 11+x²

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

11+x² =y

Multiply both sides by 1+x²

1=y(1+x²)

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

Discriminant 1=y(1+x²): −4y²+4y

−4y²+4y≥ 0 : 0≤ y≤ 1

Check if the range interval endpoints are included

y=0 : Excluded

y=1 : Included

Therefore the range is

0<f(x)≤ 1

Solve instead

domain 11+x²

inverse 11+x²

intercepts 11+x²

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

inversa 2^{x-3}

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inversa 2^{x-3}

Solution

Solution steps

Solve instead

Number Line

Graph