range of (\frac{5x+2)/(7x)}{2x}

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

☐²

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√☐

^□√☐

□□

log_□

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ddx

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

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range 5x+27x 2x

Solution

f(x)≥ −25112

Interval Notation

[−25112 , ∞ )

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Function range definition

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

Rewrite as

5x+27x 2x =y

Simplify 5x+27x 2x : 5x+214x²

5x+214x² =y

Multiply both sides by x²

5x+214 =yx²

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

Discriminant 5x+214 =yx²: 25+112y

25+112y≥ 0 : y≥ −25112

Check if the range interval endpoints are included

y=−25112 : Included

Therefore the range is

f(x)≥ −25112

Solve instead

domain 5x+27x 2x

inverse 5x+27x 2x

intercepts 5x+27x 2x

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

range of (\frac{5x+2)/(7x)}{2x}

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