Question

Sendo f(x)= x^2-2xeg(x) =x+2, determine: a) f o g (x); b) g o f (x);c) f o f (x) e g o g (x)

Answer 1

fog (x) = g²-2g
(x+2)²-2(x+2)
x²+4x+4 -2x-4
x² +2x

b) g o f (x) = f +2 = x²-2x +2

c) f o f (x) = f²-2f
(x²-2x)² -2(x²-2x)
x⁴-4x³+4x² -2x²+4x
x⁴-4x³+2x²+4x

d) g o g (x) = g +2 = x+2 +2 = x+4