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.
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)