Let's start with the initial function given:
[tex]\[ f(x) = 0.11 \cdot 3^x \][/tex]
### Step 1: Reflecting [tex]\( f(x) \)[/tex] over the [tex]\( x \)[/tex]-axis to obtain [tex]\( g(x) \)[/tex]
Reflecting a function over the [tex]\( x \)[/tex]-axis involves multiplying the function by [tex]\(-1\)[/tex]. Therefore, the function [tex]\( g(x) \)[/tex] after reflection over the [tex]\( x \)[/tex]-axis will be:
[tex]\[ g(x) = -f(x) = -0.11 \cdot 3^x \][/tex]
### Step 2: Reflecting [tex]\( g(x) \)[/tex] over the [tex]\( y \)[/tex]-axis to obtain [tex]\( h(x) \)[/tex]
Reflecting a function over the [tex]\( y \)[/tex]-axis involves replacing [tex]\( x \)[/tex] with [tex]\(-x\)[/tex]. Applying this transformation to [tex]\( g(x) \)[/tex]:
[tex]\[ h(x) = g(-x) \][/tex]
Substitute [tex]\(-x\)[/tex] into the expression for [tex]\( g(x) \)[/tex]:
[tex]\[ h(x) = -0.11 \cdot 3^{-x} \][/tex]
Thus, the function [tex]\( h(x) \)[/tex] after reflecting [tex]\( g(x) \)[/tex] over the [tex]\( y \)[/tex]-axis is:
[tex]\[ h(x) = -0.11 \cdot 3^{-x} \][/tex]
### Conclusion
After performing the reflections as described, the function [tex]\( h(x) \)[/tex] is:
[tex]\[ h(x) = -0.11 \cdot 3^{-x} \][/tex]
Among the given options, this corresponds to:
[tex]\[ \boxed{h(x) = -0.11 \cdot 3^{-x}} \][/tex]
