280106lb 280106lb
  • 15-01-2022
  • Mathematics
contestada

f(x)=2x-3 g(x)=x^2+2
Find fg(x)=gf(x)

Respuesta :

Kaprikorn
Kaprikorn Kaprikorn
  • 16-01-2022

Answer:

x = 1, 5

Step-by-step explanation:

f(g(x)) = 2(x^2+2)-3

= 2x^2+4-3

= 2x^2+1

g(f(x)) = (2x-3)^2+2

= 4x^2-12x+9+2

= 4x^2-12x+11

f(g(x)) = g(f(x))

2x^2+1 = 4x^2-12x+11

2x^2 = 4x^2-12x+11-1

2x^2 = 4x^2-12x+10

x^2 = (4x^2-12x+10)/2

x^2 = 2x^2-6x+5

x^2-2x^2 = -6x+5

-x^2 = -6x+5

x^2+6x-5 = 0

(x-1)(x-5) = 0

x-1 = 0 or x-5 = 0

x = 1 or x = 5

x = 1, 5

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