Let the function f(x) defined as \(f(x)=\frac{x-|x|}{x}\), then

Question

Question

This question was previously asked in

45th BPSC Prelims (Held in 2002) Official paper

Answer 1

The correct answer is option 4.

Given: \(f(x)=\dfrac{x-|x|}{x}\)

Calculation:

⇒ \(f(x)=\dfrac{x-|x|}{x}\)

For the value of x = 2

The function f(2) = \(\dfrac{2-|2|}{2}\) = 0

For the value of x = 0; f(0) = \(\dfrac{0-|0|}{0}\) = Impossible value

For the value of x = -2; f(-2) = \(\dfrac{-2-|-2|}{-2}\) = 2

So, the function has some definite solution for all the values of x except x = 0.

Hence, the function is a continuous function for all the values of x except x = 0.