Determine if Odd, Even, or Neither f(x) = square root of x

Problem

ƒ(x)=√(,x)

Solution

1. Identify the domain of the function ƒ(x)=√(,x) Since the square root is only defined for non-negative real numbers in the real number system, the domain is x≥0

2. Check for symmetry requirements. For a function to be even or odd, its domain must be symmetric about the origin (if x is in the domain, then −x must also be in the domain).

3. Evaluate the function at −x For any x>0 the value −x is not in the domain of ƒ(x)=√(,x)

4. Compare ƒ*(−x) to ƒ(x) and −ƒ(x) Since ƒ*(−x) is undefined for x>0 the conditions ƒ*(−x)=ƒ(x) (even) and ƒ*(−x)=−ƒ(x) (odd) cannot be satisfied for all x in the domain.

Final Answer

ƒ(x)=√(,x)* is neither odd nor even

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