Math  /  Algebra

QuestionGiven that f(x)=4x+4f(x)=4 x+4 and g(x)=x2+4xg(x)=x^{2}+4 x, find the functions below. Simplify answers completely. (a) (fg)(x)=(f \circ g)(x)= \square (b) (gf)(x)=(g \circ f)(x)= \square

Studdy Solution
Expand (4x+4)2 (4x + 4)^2 :
(4x+4)2=(4x)2+24x4+42=16x2+32x+16 (4x + 4)^2 = (4x)^2 + 2 \cdot 4x \cdot 4 + 4^2 = 16x^2 + 32x + 16
Now substitute back into the expression:
16x2+32x+16+16x+16 16x^2 + 32x + 16 + 16x + 16
Combine like terms:
16x2+48x+32 16x^2 + 48x + 32
Thus, the function (gf)(x) (g \circ f)(x) is:
16x2+48x+32 \boxed{16x^2 + 48x + 32}

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