Question

3. Sean f y g dos funciones reales definidas por :
f(x) = ax+b g(x)= x+1
Si (f o g)(3) = 11 (g o f) (2)=3
Hallar a-b

Answer 1

Respuesta:

9

Explicación paso a paso:

f(x) = ax + b

g(x) = x + 1

f(g(x)) = f(x + 1) = a(x + 1) + b

g(f(x)) = g(ax + b) = (ax + b) +1

f(g(3)) = 11

a(3 + 1) + b = 11

4a + b = 11

b = 11 - 4a

g(f(2)) = 3

a(2) + b = 3

2a + b = 3

b = 3 - 2a

b = b

11 - 4a = 3 - 2a

2a = 8

a = 4

b = 3 - 2a

b = 3 - 2(4)

b = 3 - 8

b = -5

a = 4

b = -5

a - b = 4 - (-5) = 4 + 5 = 9