Exercícios da Página 58 e 59

Ex.: 48
a) f(g(x)) = f(x-1) = 5(x-1)-6 = 5x-1-6 = 5x-7

b) g(f(x)) = g(5x-6)-5 = 5x-11

Ex.: 49
a) (f o g)(x) = f(g(x)) = f(2x+1) = (2x+1)² -2 = 4x²+4x+1-2 = 4x²=4x-1

b) (g o f)(x) = g(f(x)) = g(x²-2) = 2(x²-2)+1 = 2x²=4+1 = 2x²-3

Ex.: 50
a) f(g(1)) = x(2x+1)² -2(2x+1)+1 = x(4x²+4x+1)-4x-2+1) = 1(4+4+1)-4-2+1 = 9-4-2+1 = 4

b) g(f(2)) = 2(x²-2x+1)+1 = 2(4-4+1)+1 = 2.1+1 = 3

c)(x²-2x+1)²+2(x²-2x+1)+1 x^4+4x+1+2(x²)(-2x)+2x²+2(-2x)+ 2(X²-2X+1)+1
x^4+4x+1-4x³+2x²-4x+2(X²-2X+1)+1
1+4+1-4+2-4+2(x²-2x+1)+1
0+2*0+1=1

Ex.: 55
a) y = x-6 = x = y-6 = y = x+6 = f-¹(x) = x+6

b) y = 1-2x = x = 1-2y = y = 1-x/2 = f-¹(x) = 1-x/2

c) y = 3x+4 = x = 3y+4 = y = 3x+4 = f-¹(x) = x-4/3

d) y = 3x = x = 3y = y = 3x = f-¹(x) = x/3

Ex.: 56
x = y/y-2 = xy-2x = y = xy-y = 2x = y(x-1) = 2x = y(x-1)/2 = x = y = 2x/x-1

Ex.: 57

a) f(x) = y = 3x - 4 = x = 3y-4 = 3y = x+4 = y = x+4/3

b) f-¹(2) = y = 3(2)-4y = 6-4y = 2

Ex.: 58
a) g(x) = f-¹(x) = y = 2x+5 = x = 2y+5 = 2y = x-5 = y = x-5/2

b) (f o g) 2x-5 = x-5/2 = 2x/x-2 = x/x = x
(g o f) x-5/2 = 2x-5 = x-5/2/2x-5 = x-2/2x = x/x = x