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vertices x^2+2x-1-(2x^2-3x+6)

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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

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intervalo 19+x²

Solution

0<f(x)≤19

Interval Notation

(0, 19 ]

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Solution steps

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Definição de imagem de função

O conjunto de valores da variável dependente para a qual uma função é definida

Reescrever como

11+x² =y

Multiplicar ambos os lados por 1+x²

1=y(1+x²)

A imagem é o conjunto de 'y' para os quais o discriminante é maior ou igual a zero

Discriminante 1=y(1+x²): −4y²+4y

−4y²+4y≥ 0 : 0≤ y≤ 1

Verificar se os pontos finais do intervalo da imagem estão inclusos

y=0 : Excluído

y=1 : Incluído

Portanto, a imagem é

0<f(x)≤ 1

Solve instead

domínio 19+x²

inversa 19+x²

interceptos 19+x²

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

vertices x^2+2x-1-(2x^2-3x+6)

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