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