Question

Need help determining if h. F(x)= 3^x is even, odd or neither

Answer 1

Recall that:

1) f(x) is an even function if:

`f(-x)=f\mleft(x\mright).`

2) f(x) is an odd function if:

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

Now, notice that:

`\begin{gathered} f(-x)=3^(-x)\\e3^x=f(x), \\ f(-x)=3^(-x)\\e-3^x=-f(x). \end{gathered}`

Therefore f(x)=3^x is neither an even function nor an odd function.

Answer: Neither an even function nor an odd function.