To determine the cost of mulch based on the radius [tex]\(x\)[/tex] of the circle, let's follow the given functions step by step:
1. Calculate the area requiring mulch, [tex]\(m(x)\)[/tex]:
The function [tex]\(m(x)\)[/tex] gives the area needing mulch:
[tex]\[
m(x) = \pi x^2 - 2 \sqrt{2} x^2
\][/tex]
2. Calculate the cost based on the area, [tex]\(g(m)\)[/tex]:
The cost function [tex]\(g(m)\)[/tex] is given as:
[tex]\[
g(m) = 1.50 m
\][/tex]
3. Combine the functions:
The cost of the mulch, based on the radius [tex]\(x\)[/tex] of the circle, can be represented by substituting [tex]\(m(x)\)[/tex] into [tex]\(g(m)\)[/tex]:
[tex]\[
g(m(x)) = 1.50 \left(\pi x^2 - 2 \sqrt{2} x^2\right)
\][/tex]
Therefore, the expression representing the cost of the mulch based on the radius of the circle is:
[tex]\[
1.50\left(\pi x^2 - 2 \sqrt{2} x^2\right)
\][/tex]
So, the correct choice is:
[tex]\[
\boxed{1.50\left(\pi x^2-2 \sqrt{2} x^2\right)}
\][/tex]