Question

Express your answer as a polynomial in standard form.
f(x)=−4x+8,g(x)=x²-2x+1. Find: (f∘g)(x).

Answer 1

To find (f \circ g)(x), we apply f(x) to g(x). The function g(x) is x^2 - 2x + 1 and f(x) is -4x + 8. Applying f to g, we get the polynomial -4x^2 + 8x + 4 in standard form. f(g(x)) = -4x2 + 8x + 4

Step-by-step explanation:

To find the composite function (f \circ g)(x), first apply the function g(x) and then apply f(x) to the result. We are given f(x) = -4x + 8 and g(x) = x2 - 2x + 1. Let's calculate g(x) first:

g(x) = x2 - 2x + 1

Now apply f(x) to g(x):

f(g(x)) = f(x2 - 2x + 1)

Replace x in f(x) with x2 - 2x + 1:

f(g(x)) = -4(x2 - 2x + 1) + 8

Distribute the -4:

f(g(x)) = -4x2 + 8x - 4 + 8

Combine like terms:

f(g(x)) = -4x2 + 8x + 4

This is the polynomial in standard form for the composite function (f \circ g)(x).