Function f(x) = |px - q| + r|x|,x ∈ ( - ∞ ,∞ ) , where p > 0,q > 0,r

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1.Relation and Function

medium

The function $f(x) = \;|px - q|\; + r|x|,\;x \in ( - \infty ,\;\infty )$, where $p > 0,\;q > 0,\;r > 0$ assumes its minimum value only at one point, if

$p \ne q$

$q \ne r$

$r \ne p$

$p = q = r$

(IIT-1995)

Solution

(d)The function $f(x) = \,\,|\,\,px – q\,\,| + r|x|,\,\,x \in ( – \infty ,\,\,\infty )$ where $p > 0,\,\,q > 0,\,\,r > 0$ can assume its minimum value only at one point, if $p = q = r.$

Standard 12

Mathematics

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