Step 1 :The function is defined as \(f(x)=4^{x}\).
Step 2 :To find \(f(1)\), we substitute \(x=1\) into the function, giving us \(4^{1} = 4\).
Step 3 :To find \(f(-1)\), we substitute \(x=-1\) into the function, giving us \(4^{-1} = 0.25\).
Step 4 :Final Answer: \(f(1) = \boxed{4}\) and \(f(-1) = \boxed{0.25}\)