9514 1404 393
Answer:
x -1
Step-by-step explanation:
The absolute value function is piecewise linear. When its argument is negative, it gives the opposite of that argument:
|x| = -x . . . for x < 0
|x| = x . . . for x ≥ 0
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When the argument is some function of x, the same rules apply.
|x -1| = -(x -1) . . . for (x -1) < 0
|x -1| = x -1 . . . for x -1 > 0
The condition x-1 > 0 is equivalent to x > 1, so you have ...
|x -1| = x -1 . . . for x > 1
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The attached graph shows that |x-1| and x-1 are the same graph when x>1.
