Given,

2^{x + 1} + 2^x = 3

Now simplifying:

⇒ 2 × 2^x + 2^x = 3

⇒ 2^x(2 + 1) = 3

⇒ 2^x × 3 = 3

⇒ 2^x = 1

⇒ 2^x = 2⁰

Equating the exponents:

⇒ x = 0

Substituting value of x in 3^x + 3^-x, we get :

⇒ 3⁰ + 3⁰

⇒ 1 + 1

⇒ 2.

Hence, option 3 is the correct option.