The minimum value of $f (x) = | 3 - x | + | 2 + x | + | 5 - x |$ is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 7
$f (x) = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 6 - 3 x & x < - 2 10 - x & - 2 < x < 3 4 + x & 3 < x < 5 3 x - 6 & x > 5 \end{matrix}$
$f^{1} (x) = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} - 3 & x < - 2 - 1 & - 2 < x < 3 1 & 3 < x < 5 3 & x > 5 \end{matrix}$
So $f (x)$ is minimum at $x = 3$
$f (3) = 7$

Suggest Corrections

Similar questions

f (x) = | 3 - x | + | 2 + x | + | 5 - x |

f (x) = | x - 1 | + | x - 2 | + | x - 3 |

f (x) = | x - 1 | + | x - 2 | + | x - 3 |

f (x) = x + \frac{4}{x + 2}

f (x) = \frac{(x - 2) (x - 1)}{(x - 3)} \forall x > 3

Join BYJU'S Learning Program