Respuesta :
Answer:
x = 0, x = - 2
Step-by-step explanation:
Find g(f(x)) and f(g(x))
g(f(x)) = g(2x + 1) = (2x + 1)²
f(g(x)) = f(x²) = 2x² + 1
Thus
(2x + 1)² = 2x² + 1 ← expand left side using FOIL
4x² + 4x + 1 = 2x² + 1 ← subtract 2x² + 1 from both sides
2x² + 4x = 0 ← in standard form
2x(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
x + 2 = 0 ⇒ x = - 2
WRONG ANSWER
I did not read fg(x) and gf(x) but only g(x) and f(x)!!!!
Answer:
x₁= 1-√2 and x₂=1+√2
Step-by-step explanation:
you need to find where the system of the two given equation has solutions
one equation is linear, the other one is a parabolic equation, there will be at most 2 points where they cross path (but there could be even 1 point or even none)
you need to find where 2x+1 = x^2 or x^2-2x -1 = 0
using the quadratic formula x=(−b±√b2−4ac)/2a
a=1 b=-2 c=-1
you will get two solutions x₁= 1-√2 and x₂=1+√2
