let the closed interval [a,b] be the domain of the function f find the domain of f(x−3) and f(x+3) ?


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Question Number 192732 by mokys last updated on 25/May/23

$l e t t h e c l o s e d i n t e r v a l [a, b] b e t h e d o m a i n o f t h e f u n c t i o n f$ $f i n d t h e d o m a i n o f f (x - 3) a n d f (x + 3) ?$
	Answered by MM42 last updated on 25/May/23

	$a ⩽ x - 3 ⩽ b \Rightarrow a + 3 ⩽ x ⩽ b + 3 \Rightarrow D_{f - 3} = [a + 3, b + 3]$ $a ⩽ x + 3 ⩽ b \Rightarrow a - 3 ⩽ x ⩽ b - 3 \Rightarrow D_{f + 3} = [a - 3, b - 3]$
	Answered by Rajpurohith last updated on 26/May/23

	$s o f o r a ⩽ x ⩽ b, f (x) i s d e f i n e d$ $\Rightarrow f o r a - 3 ⩽ x - 3 ⩽ b - 3, f (x - 3) i s d e f i n e d .$ $\Rightarrow f o r a + 3 ⩽ x + 3 ⩽ b + 3, f (x + 3) i s d e f i n e d .$
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