It is given that
[tex]\begin{gathered} g(x)=3(2^{x)\text{ }}and\text{ h}(x)=2^{x-1} \\ \text{And we n}ed\text{ to find k(x)=(g-h)(x)} \end{gathered}[/tex]
Now
[tex]\begin{gathered} k(x)=(g-h)(x) \\ =g(x)-h(x) \\ =3(2^x)-(2^{x-1)^{}} \\ =2^x(3-\frac{1}{2}) \\ =2^x(\frac{6-1}{2}) \\ =2^x(\frac{5}{2)} \\ =5(2^{x-1}) \end{gathered}[/tex]
So the correct option is
[tex]5(2^{x-1})[/tex]
