Question

find the range of f(x)=|x-1| +|x-2|;x € (-13]​

Answer 1

Answer:

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When x ∈ (-∞,1), f(x) = (1-x) + (2-x) = 3–2x ………..(a)

When x ∈ [1,2), f(x) = (x-1) + (2-x) = 1 …………….(b)

When x ∈ [2,∞), f(x) = (x-1) + (x-2) = 2x - 3 …………(c)

So, it is evident from (a), (b) and (c) that the minimum value of f(x) is attained for x ∈ [1,2) and it is equal to 1.

Considering (c), we find that as x -> ∞, f(x) -> ∞, and from equation (a), we find that as x -> -∞, f(x) -> ∞.

Hence, the range of f(x) is [1,∞)

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Answer 2

Answer:

Step-by-step explanation: