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f(x)=|a x-b|+c|x|AAx in (-oo,oo), where ...

`f(x)=|a x-b|+c|x|AAx in (-oo,oo),` where `a >0, b >0,c > 0.` Find the condition if `f(x)` attains the minimum value only at one point.

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To find the condition under which the function \( f(x) = |ax - b| + c|x| \) attains its minimum value only at one point, we can analyze the function step by step. ### Step 1: Break down the function based on the absolute values The function \( f(x) \) can be expressed in piecewise form based on the values of \( x \): 1. **For \( x < 0 \)**: \[ f(x) = |ax - b| + c|x| = (b - ax) + (-cx) = b - ax - cx = b - (a + c)x ...
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