Question

How to find the Domain of the Function of X such that F(X)=1/√|X|-X..? Please hurry..!!​

Answer 1

Answer:

What is the domain of the function Y=1/√|x|-x?

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We know that element inside the square root should be greater than or equal to zero .

But in this case since square root is in denominator it can't be equal to zero .

So in this case element inside the square root should be greater than zero .

i.e |x| - x > 0

Now here arises two cases x>0 and x<0

1st case x>0

In this case |x| = x

Therefore equation becomes x - x > 0

=> 0 > 0 Now this is an absurd result or we can say x can't lie in this range

2nd case x<0

In this case |x| = -x ( because x is negative and multiplying it with -1 will make it positive)

So the equation becomes - x - x > 0

=> - 2x > 0 => x < 0

Hence all value less than zero satisfies the equation .

Now we have to take union of the two cases which results in x<0

Thus x can be anything from - infinity to 0 but not 0

Thus domain of function is (- infinity , 0) , 0 is excluded .

Hope it helps !!!

Step-by-step explanation:

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