# Q. 4 Show that the function defined by      is one one and onto function.

The function    defined by

,

One- one:

Let                  ,

It is observed that if x is positive and y is negative.

Since x is positive and y is negative.

but 2xy is negative.

Thus, the case of x is positive and y is negative is removed.

Same happens in the case  of y is positive and x is negative so this case is also removed.

When x and y both are positive:

When x and y both are negative

f is one-one.

Onto:

Let    such that

If y is negative, then

If y is positive, then

Thus, f is onto.

Hence, f is one-one and onto.

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