MGF Question

Before I try computing the expectation as per the question requirement, I would like to confirm if the MGF I have derived is correct?

My answer after:

$\displaystyle =\int e^{tx}\ f(x)\ dx$

$\displaystyle =\frac{(3t-1)e^t + (1-t)e^{-t}}{4t^2}$

Thank you