MATH SOLVE

4 months ago

Q:
# even function neither even nor odd odd function both even and odd F(X)=X2+3

Accepted Solution

A:

We have the following definitions:

A function is even if, for each x in the domain of f, f (- x) = f (x). The even functions have reflective symmetry through the y-axis.

A function is odd if, for each x in the domain of f, f (- x) = - f (x). The odd functions have rotational symmetry of 180º with respect to the origin.

We have then:

F (-X) = (- X) 2 + 3

Rewriting:

F (-X) = (X) 2 + 3

F (-X) = F (X)

Answer:

F (-X) = F (X)

The function is even according to the definition:

A function is even if, for each x in the domain of f, f (- x) = f (x). The even functions have reflective symmetry through the y-axis.

A function is odd if, for each x in the domain of f, f (- x) = - f (x). The odd functions have rotational symmetry of 180º with respect to the origin.

We have then:

F (-X) = (- X) 2 + 3

Rewriting:

F (-X) = (X) 2 + 3

F (-X) = F (X)

Answer:

F (-X) = F (X)

The function is even according to the definition: