Answer:
[tex]m(r(x)) = -0.000105156(x-50)^2 + 0.64008[/tex]
Step-by-step explanation:
Composite Function
The composition of functions f(x) and g(x) is denoted as [tex](f\circ g)(x)[/tex] and can be obtained by the expression
[tex]f\circ g(x)=f(g(x))[/tex]
In practice, it means to replace into each x of f, the whole expression for g.
We know the function
[tex]r(x) = -0.000345(x-50)^2 + 2.1[/tex]
can be used to model some reality, being x in feet. We also know that another function
[tex]m(x) = 0.3048x[/tex]
is going to be used to convert feet to meters. We are required to find
[tex]m\circ r(x)=m(r(x))[/tex]
We'll replace the expression for r into m as:
[tex]m(x) = 0.3048\left[-0.000345(x-50)^2 + 2.1\right][/tex]
Operating
[tex]\boxed{m(r(x)) = -0.000105156(x-50)^2 + 0.64008}[/tex]
