You can see that the graph of [tex] g(x) [/tex] is the graph of [tex] f(x) [/tex] translated one unit to the left.
Horizontal translations are given by the transformation
[tex] f(x) \mapsto f(x+k) [/tex]
If [tex] k>0 [/tex] the function is translated k units to the left, else if [tex] k<0 [/tex] the function is translated k units to the right.
So, in your case, [tex] k=1 [/tex]
And thus you have
[tex] g(x) = f(x+1) = 2^{x+1} [/tex]
