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domain of (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`)

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ddx

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

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intervalo x²+1x²−x−6

Solution

f(x)≤−2√2+25 or f(x)≥2√2+25

Interval Notation

(−∞ , −2√2+25 ]∪ [2√2+25 , ∞ )

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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

x²+1x²−x−6 =y

Multiplicar ambos os lados por x²−x−6

x²+1=y(x²−x−6)

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

Discriminante x²+1=y(x²−x−6): 25y²−20y−4

25y²−20y−4≥ 0 : y≤ −2√2+25 or y≥ 2√2+25

Verificar se os pontos finais do intervalo da imagem estão inclusos

y=−2√2+25 : Incluído

y=2√2+25 : Incluído

Portanto, a imagem é

f(x)≤ −2√2+25 or f(x)≥ 2√2+25

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domínio x²+1x²−x−6

inversa x²+1x²−x−6

interceptos x²+1x²−x−6

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

domain of (x^2+2x-1)*(2x^2-3x+6)

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domain of (x^2+2x-1)*(2x^2-3x+6)

Solution

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