Answer:
x = - 2 , 0
Explanation:
to find f(g(x)) substitute x = g(x) into f(x)
f(g(x))
= f(x²)
= 2x² + 1
to find g(f(x)) substitute x = f(x) into g(x)
g(f(x))
= g(2x + 1)
= (2x + 1)²
= 4x² + 4x + 1
now equate the 2 expressions
4x² + 4x + 1 = 2x² + 1 ( subtract 2x² from both sides )
2x² + 4x + 1 = 1 ( subtract 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
then x = - 2 , 0