How do you write #f(x) = 1 - |x - 1|# as a piecewise function?

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Answer 1 · 2016-06-23T08:04:42

Piecewise, #f(x)=x, x in (-oo, 1] and f(x)=2-x, x in [1, oo)#.

#|x-1|=1-x, x in (-oo, 1] and

#=x-1, x in [1, oo)#.

So,

#f(x)=x-(1-x)=x, x in (-oo, 1]#

#=1-(x-1)=2-x, x in [1, oo)#.

Note that f(x) is continuous everywhere.

The graph is collar (inverted V)-like, with vertex at (1, 1).