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Given-the-function-f-defined-by-f-x-x-2-1-x-i-state-the-domain-of-f-ii-show-that-f-x-2-x-1-x-x-lt-0-2-x-1-x-0-x-lt-2-x-2-1-x-x-2-

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Question Number 94078 by Rio Michael last updated on 16/May/20
Given the function f defined by f(x) = ((∣x−2∣)/(1−∣x∣)) (i) state the domain of f. (ii) show that f(x) = { ((((2−x)/(1+x)) , x < 0)),((((2−x)/(1−x)), 0 ≤ x < 2)),((((x−2)/(1−x)) , x ≥ 2)) :} (iii) Investigate the continuity of f at x = 2.
Giventhefunctionfdefinedbyf(x)=∣x−2∣1−∣x∣(i)statethedomainoff.(ii)showthatf(x)={2−x1+x,x<02−x1−x,0⩽x<2x−21−x,x⩾2(iii)Investigatethecontinuityoffatx=2.

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