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domain of tan(2x-5)

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domain tan(2x−5)

Solution

π2 n≤ x<10−3π4 +π2 n or 10−3π4 +π2 n<x<π2 +π2 n

Interval Notation

[π2 n, 10−3π4 +π2 n)∪(10−3π4 +π2 n, π2 +π2 n)

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Domain definition

The domain of a function is the set of input or argument values for which the function is real and defined

Take the denominator(s) of tan(2x−5) and compare to zero: x=10−3π4 +π2 n

Periodicity of tan(2x−5): π2

Combine period: π2 n≤ x<π2 +π2 n and undefined points.
The domain is

π2 n≤ x<10−3π4 +π2 n or 10−3π4 +π2 n<x<π2 +π2 n

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range tan(2x−5)

periodicity tan(2x−5)

amplitude tan(2x−5)

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

domain of tan(2x-5)

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