How can you tell if a mathematical function to ODD, EVEN, or nothing?

What's this? g (x) = – f (x) + 1 if f (x) is an even function, which is g (x)? if f (x) is an even function, which is g (x)?

A function is even if f (x) = f (-x) and odd if f (x) = f (-x) for all x. In other words, a function is even if it is symmetrical about the axis Y, and odd if it is antisymmetric (symmetric but reversed for negative x). Of course, a function is neither funny nor even if it can not be described by one of the two equations above or descriptions. An example of an even function is cos (x), and an odd function is sin (x). Now, given your equation, g (x) = F (x) + 1 To test whether g (x) is even, we replace your equation in both sides of the equation "defintion" because even function, which is g (x) = g (x) if the function is even. substituting your equations for g (x) and g (x), we obtain-f (x) + 1 = f (-x) + 1 You state that f (x) is even, so we know that f (x) = f (-x). We replace it in the right side of the equation above and get-f (x) + 1 = f (x) + 1 We see immediately that the equation holds. We therefore conclude that g (x) is even if f (x) is even.

WJEC Further Maths – Odd and Even Functions