Question

Find the domain of the real valued function: f(x) = $\sqrt{\frac{4 - x^{2}}{[x] + 2}}$

Answer 1

Answer:

domain (f) =(-1 ,∞)

Step-by-step explanation:

To find the domain of the real valued function:

$f(x)=\sqrt{\frac{4-x^{2}}{[x]+2} }$

as we know that [x] denotes the gratest integer function{less than or equal to x}

thus here the function is under square root i.e [x]+2≠0 and  [x]+2 > 2

so [x]+2 =0,if x=-2

its domain does not include -2

and we know that underroot does not have negative values so on putting x=-1 ,the function exist

So domain (f) =(-1 ,∞)