Question

Is the function f(x) =x^2—3 even, odd , or neither ? Using algebraic to do define answer

Answer 1

Given function is

`f(x)=x^2-3`

Recall that a function f(x) is even if f(-x)=f(x) for all x, and a function f(x) is odd if f(-x)= - f(x) for all x.

Replace x=-x to check the given fuction.

`f(-x)=(-x)^2-3`

`f(-x)=x^2-3=f(x)`

`f(-x)=f(x)`

We get f(-x)=f(x).

Hence the given function is even.