next term a_{n}=(3^{n+2})/(5^n)

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range 19+x²

Solution

0<f(x)≤19

Interval Notation

(0, 19 ]

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Function range definition

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

Rewrite as

19+x² =y

Multiply both sides by 9+x²

1=y(9+x²)

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

Discriminant 1=y(9+x²): −36y²+4y

−36y²+4y≥ 0 : 0≤ y≤ 19

Check if the range interval endpoints are included

y=0 : Excluded

y=19 : Included

Therefore the range is

0<f(x)≤ 19

Solve instead

domain 19+x²

inverse 19+x²

intercepts 19+x²

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

next term a_{n}=(3^{n+2})/(5^n)

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