The minimum value of the expression is y - x -1- x -3- isA- 0B- 1C- 5D- 4

The correct option is D 4y=|x+1|+|x 3| Here the turning points are 1, 3 y = (x+1) (x 3), amp;x 1 (x+1) (x 3), amp; 1≤ x3 (x+1)+(x 3), amp;x≥3 ⇒ y = ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Absolute Value Function

The minimum v...

Question

The minimum value of the expression is $y = | x + 1 | + | x - 3 |$ is

0

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

1

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

4

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

5

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

Open in App

Solution

The correct option is C $4$
$y = | x + 1 | + | x - 3 |$
Here the turning points are $- 1, 3$
$y = ⎧ ⎨ ⎩ \begin{matrix} - (x + 1) - (x - 3), & x < - 1 (x + 1) - (x - 3), & - 1 \leq x < 3 (x + 1) + (x - 3), & x \geq 3 \end{matrix} \Rightarrow y = ⎧ ⎨ ⎩ \begin{matrix} 2 - 2 x, & x < - 1 4, & - 1 \leq x < 3 2 x - 2, & x \geq 3 \end{matrix}$

Hence, the minimum value of the expression is $4$ .

Suggest Corrections

Similar questions

The minimum value of the function defined by f(x) = minimum {x, x+1,2 - x } is

Q. For all real x, the minimum value of

\frac{1 - x + x^{2}}{1 + x + x^{2}}

Q. The value(s) of

x

for which the expression

y = | x + 2 | + | x - 7 |

is minimum is/are

If x =2, y = -1, then the value of $x^{2} + 4 x y + 4 y^{2}$ is

The value of the expression $16 x^{2} + 24 x + 9$ for $x = 0$ is _____.

Join BYJU'S Learning Program

Explore more

Absolute Value Function

Standard XII Mathematics

Join BYJU'S Learning Program

The minimum value of the expression is y=|x+1|+|x−3| is

The correct option is C 4y=|x+1|+|x−3| Here the turning points are −1,3 y=⎧⎨⎩−(x+1)−(x−3),x<−1(x+1)−(x−3),−1≤x<3(x+1)+(x−3),x≥3⇒y=⎧⎨⎩2−2x,x<−14,−1≤x<32x−2,x≥3 Hence, the minimum value of the expression is 4.

The minimum value of the expression is $y = | x + 1 | + | x - 3 |$ is