Answer:
[tex](g\ o\ f)=-20x+10[/tex]
Step-by-step explanation:
One is given the following functions:
f(x) =5x + 2
g(x) = 4x + 2
One is asked to find the following:
[tex](g\ o\ f)(x)[/tex]
One can rewrite this operation as the following:
g(f(x))
In essence, one substitutes in function (g) in place of the parameter (x), and solves to find the new function formed.
[tex]g(f(x))\\\\=g(-5x+2)\\\\=4(-5x+2)+2[/tex]
Simplify, distribute, multiply every term in the parenthesis by the term outside of it, then simplify,
[tex]=-20x+8+2\\\\=-20x+10[/tex]
