Given the function f(x) = x^2/sqrt(1+x)

We need to find the domain of f(x).

The domain of the function is all x values such that the function is defined.

But, since the the function is a quotient, then we know that the denominator can not be 0.

Also, the denominator is a square root. Then, we know that the square root muts be a values equal or greater than 0.

Then the denominator must be greater that 0.

==>sqrt(1+x) > 0

==> (1+x) > 0

==> x > -1

Then, the domain of the function f(x) is all real numbers greater than -1.

**==> The domain = (-1 , inf)**

For a function f(x), the domain is the set of values of x for which the value of f(x) is real.

We have f(x) = x^2/ sqrt (1 + x).

x^2 is always real and sqrt (1 + x) is real for all values of x such that (1+x) >0

=> 1 > -x

=> x > -1

**Therefore the required domain is all values of x greater than -1.**