[tex]w(f(m(2))) = 593[/tex]
We can write how [tex]w(f(m(x)))[/tex] will be defined but that's too much work and it's only useful when we are evaluating [tex]w(f(m(x)))[/tex] with many inputs.
First let's solve for [tex]m(2)[/tex] first. As you read through this answer, you'll get the idea of what I'm doing.
Given:
[tex]m(x) = -4x +1[/tex]
Solving for [tex]m(2)[/tex]:
[tex]m(2) = -4(2) +1 \\ m(2) = -8 +1 \\ m(2) = -7[/tex]
Now we can solve for [tex]f(m(2))[/tex], since [tex]m(2) = -7[/tex], [tex]f(m(2)) = f(-7)[/tex].
Given:
[tex]f(x)=3x-1[/tex]
Solving for [tex]f(-7)[/tex]:
[tex]f(-7)=3(-7)-1 \\ f(-7) = -21 -1 \\ f(-7) = -22[/tex]
Now we are can solve for [tex]w(-22)[/tex]. By now you should get the idea why [tex]w(f(m(2))) = w(-22)[/tex].
Given:
[tex]w(x) = x^2 -5x -1[/tex]
Solving for [tex]w(-22)[/tex]:
[tex]w(-22) = (-22)^2 -5(-22) -1 \\ w(-22) = 484 -5(-22) -1 \\ w(-22) = 484 +110 -1 \\ w(-22) = 593[/tex]
