Question

How to determine if a function is even or odd calculus?

Answer 1

To determine if a function is even, check if it satisfies the equation f(x) = f(-x) for all x-values. If it does, then the function is even. To determine if a function is odd, check if it satisfies the equation f(x) = -f(-x) for all x-values. If it does, then the function is odd.

Step-by-step explanation:

An even function is a function where the output values remain the same when the input values are replaced by their negatives. In other words, the graph of an even function is symmetric with respect to the y-axis. One way to determine if a function is even is to check if it satisfies the equation f(x) = f(-x) for all values of x. If this equation holds true, then the function is even. On the other hand, an odd function is a function where the output values become negative when the input values are replaced by their negatives. The graph of an odd function is symmetric with respect to the origin. To determine if a function is odd, we need to check if it satisfies the equation f(x) = -f(-x) for all values of x. If this equation holds true, then the function is odd.

Answer 2

A function
`f(x)` is even if
`f(-x)=f(x)`, and is odd if
`f(-x)=-f(x)`.

Example:


`f(x)=x^2` is even, since
`f(-x)=(-x)^2=x^2=f(x)`.


`g(x)=x^3-x` is odd, since
`g(-x)=(-x)^3-(-x)=-x^3+x=-(x^3-x)=-g(x)`.