Question

$\huge\red{Question}$

Find the domain and range of the function
$f(x) = \frac{ {x}^{2} }{1 + {x}^{2} }$
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Answer 1

Given function is,

x^2/(1+x^2)

For this function to be real, the denominator mustn't be zero.

Now, look at the denominator carefully.

Do you think it can ever be zero?

Nay, it can never be equal to zero for any real value of x.

Reason: x^2 is always a positive integer(quite obvious) and when 1 is added to a positive integer (here x^2), the result will always be positive. It can neither be negative nor zero.

Thereby, we can say that the function x^2/(1+x^2) gives a real value for each and every real value if x.

Hence, the domain of this function is R or set of all real numbers.