We will graph each case to determine the solution to the problem
using a graph tool
case a) \(f(x)=2( \frac{1}{2}^{x})\)
see the attached figure N \(1\)
case b) \(f(x)=\frac{1}{2} (2^{x} )\)
see the attached figure N \(2\)
case c) \(f(x)= \frac{1}{2} (\frac{1}{2}^{x})\)
see the attached figure N \(3\)
case d) \(f(x)=2 (2^{x})\)
see the attached figure N \(4\)
therefore
the answer is
case b) \(f(x)=\frac{1}{2} (2^{x} )\)
