Answer:
x = 0, - 2
Step-by-step explanation:
To find f(g(x)) , substitute x = g(x) into f(x)
f(x²) = 2x² + 1
To find g(f(x)) , substitute x = f(x) into g(x)
g(2x + 1) = (2x + 1)²
Then equating
(2x + 1)² = 2x² + 1 ← expand left side using FOIL
4x² + 4x + 1 = 2x² + 1 ( subtract 2x² + 1 from both sides )
2x² + 4x = 0 ← factor out 2x from each term on the left side
2x(x + 2) = 0
Equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
x + 2 = 0 ⇒ x = - 2
solutions are x = 0, - 2
