Question

What is the value of a if h is an even function

Answer 1

Step 1: Write out the expression for even function

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

Now, substitute the values in the table to obey this expression above and get what a will be:

`\begin{gathered} f(x)=f(-x) \\ \text{when x=4, y =}(1)/(2) \\ (1)/(2)(4)=(1)/(2)(-4) \\ \\ \text{When x=-4, a = }(1)/(2) \end{gathered}`

The value of a if h is an even function is:

`(1)/(2)`

Step 2: Write out the expression for an odd function

`\begin{gathered} f(x)=-f(-x) \\ \text{When x=4, y=}(1)/(2) \\ \text{Substitute into the odd function} \\ (1)/(2)(4)=-(1)/(2)(-4) \\ \\ \text{When x=-4, a=-}(1)/(2) \end{gathered}`

The value of a if h is an odd function is:

`-(1)/(2)`