Answer:
f(g(x)) = -2x -10
Explanation:
You want to find f(g(x)) when f(x) = 2 -4x and g(x) = 1/2x +3.
Composition
The desired function of the function can be found using substitution for the argument in the usual way:
f(g(x)) = f(1/2x +3) = 2 -4(1/2x +3)
f(g(x)) = 2 -2x -12 . . . . . eliminate parentheses
f(g(x)) = -2x -10
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Additional comment
A function of a function is called a composition. This one can also be written using the ring operator.
f(g(x)) ⇔ (f∘g)(x)