Answer:
Our composed function is [tex]f(g(x)) = -4x^2-x-4[/tex].
Step-by-step explanation:
We are given two separate functions:
[tex]f(x) = 2-x[/tex]
[tex]g(x) = 4x^2 + x + 6[/tex]
We need to find the composition of [tex](f \cdot g)(x)[/tex]. This is literally stating "f of g of x."
Therefore, we simply plug g(x) into f(x) and solve. We replace the x-value in the f(x) function with the entirety of the g(x) function and simplify.
[tex]f(g(x)) = 2 - (4x^2+x+6)\\\\f(g(x)) = 2 - 4x^2 + x + 6\\\\f(g(x)) = -4x^2 - x - 4[/tex]
Our composed function is [tex]f(g(x)) = -4x^2-x-4[/tex].
