SOLUTION
Step 1: Write out the expression for even function
[tex]f(x)=f(-x)[/tex]
Now, substitute the values in the table to obey this expression above and get what a will be:
[tex]\begin{gathered} f(x)=f(-x) \\ \text{when x=4, y =}\frac{1}{2} \\ \frac{1}{2}(4)=\frac{1}{2}(-4) \\ \\ \text{When x=-4, a = }\frac{1}{2} \end{gathered}[/tex]
The value of a if h is an even function is:
[tex]\frac{1}{2}[/tex]
Step 2: Write out the expression for an odd function
[tex]\begin{gathered} f(x)=-f(-x) \\ \text{When x=4, y=}\frac{1}{2} \\ \text{Substitute into the odd function} \\ \frac{1}{2}(4)=-\frac{1}{2}(-4) \\ \\ \text{When x=-4, a=-}\frac{1}{2} \end{gathered}[/tex]
The value of a if h is an odd function is:
[tex]-\frac{1}{2}[/tex]
