Question

find domain and range of f={(x,1/1-x^2;x€R,x≠±1)}

Answer 1

Answer:

Since all real values for x except ±1 is applicable for the given f(x), the domain can be written as:

Domain = R - {±1}

We dont include ±1 because for ±1, the denominator in the function becomes 0, which leads to an indeterminate form. So ±1 is not a part of domain.

Maximum Value of Range is when x has the minimum value which is 0.

Hence Maximum value of Range when x = 0 is:

⇒ 1 / 1 - 0 = 1 / 1 = 1

Hence Maximum value it can take is 1.

Minimum value it can take can be determined if the value of x we take is maximum.

Considering x = 2, 3, ... ∞ we get the answer for the function to be,

⇒ 1 / 1 - 2² = -1 / 3

⇒ 1 / 1 - 3² = -1 / 8

So as the value gets more and more upto infinity, the value of function reduces to -1.

Hence the minimum value of the given function is -1.

Hence f(x) has a range between [ -1, 1 ]

Hope it helped !!