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

  • [IIT 1995]
  • A

    $p \ne q$

  • B

    $q \ne r$

  • C

    $r \ne p$

  • D

    $p = q = r$

Similar Questions

If $f(x)$ and $g(x)$ are functions satisfying $f(g(x))$ = $x^3 + 3x^2 + 3x + 4$  $f(x)$ = $log^3x + 3$, then slope of the tangent to the curve $y = g(x)$ at $x =  \ -1$ is 

Domain of $log\,log\,log\,  ....(x)$ is 

                        $ \leftarrow \,n\,\,times\, \to $

If $f (x) =$ $\left[ \begin{gathered}  {x^2}\,\,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,x \leqslant \,{x_0} \hfill \\   ax + b\,\,\,\,\,if\,\,\,\,x\, > \,{x_0} \hfill \\ \end{gathered}  \right.$ derivable $\forall \,x\, \in \,R\,\,$ then the values of $a$ and $b$ are respectively

Let $f(x)$ be a non-constant polynomial with real coefficients such that $f\left(\frac{1}{2}\right)=100$ and $f(x) \leq 100$ for all real $x$. Which of the following statements is NOT necessarily true?

  • [KVPY 2013]

Let $E = \{ 1,2,3,4\} $ and $F = \{ 1,2\} $.Then the number of onto functions from $E$ to $F$ is

  • [IIT 2001]