Answer
[tex]f\left(x\right)=2^{-x}+2[/tex]
Explanation
Given the parent function:
[tex]f(x)=2^x[/tex]
As the first transformation is a shift up, then it is having an impact on the y-axis, which means that we have to add two to the function as follows (if it were a shift down we would have to subtract):
[tex]h(x)=2^x+2[/tex]
Next, reflecting over the y axis is to negate the value of the x-coordinate of each point, thus:
[tex]g(x)=2^{-x}+2[/tex]
Below we can see the transformations:
