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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
let the closed interval [a,b] be the domain of the function f find the domain of f(x−3) and f(x+3) ?
lettheclosedinterval[a,b]bethedomainofthefunctionffindthedomainoff(x−3)andf(x+3)?
Answered by MM42 last updated on 25/May/23
a≤x−3≤b⇒a+3≤x≤b+3⇒D_(f−3) =[a+3,b+3] a≤x+3≤b⇒a−3≤x≤b−3⇒D_(f+3) =[a−3,b−3]
a⩽x−3⩽b⇒a+3⩽x⩽b+3⇒Df−3=[a+3,b+3]a⩽x+3⩽b⇒a−3⩽x⩽b−3⇒Df+3=[a−3,b−3]
Answered by Rajpurohith last updated on 26/May/23
so for a≤x≤b ,f(x) is defined ⇒for a−3≤x−3≤b−3 ,f(x−3) is defined. ⇒for a+3≤x+3≤b+3 ,f(x+3) is defined.
sofora⩽x⩽b,f(x)isdefined⇒fora−3⩽x−3⩽b−3,f(x−3)isdefined.⇒fora+3⩽x+3⩽b+3,f(x+3)isdefined.

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