Question

Number of values of x which satisfies the relation $|x-1|$ + $|x-2|$ =1

• A. 1
• B. 2
• C. 0
• D. Infinite

Answer 1

The correct option is D

Infinite

We will first remove the modulus and split the function.

Let f(x) = $|x-1|$ +$|x-2|$, it attains different values in different intervals.

x $\ge$ 2

if x $\ge$ 2,$|x-1|$ = x-1 and $|x-2|$= x - 2

$\Rightarrow$ f(x) = x -1 + x - 2

= 2x - 3
2x-3 = 1 gives x=2.............................(1)

1$\le$ x $\le$ 2


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

So for all the values of x between 1 and 2 the equation is satisfied.

There are infinite values of x between 1 and 2..............................(2)

For x less than or equal to 1

f(x) = 1-x +2-x
= 3-2x
3-2x = 1 gives x = 1....................(3)

From 1 ,2 and 3 we can conclude that there are infinite values of x which satisfy the equation