You can think of this either as a binomial expansion, or a Taylor expansion about x = 0. (This last is probably what your professor wants.) Either way:

f(x) (is approximately) 1 + (1/3)(3x)x + ... = 1 + x + ...

So

f(1.03) = f(1 + 3*0.01) (is approximately) 1 + 0.01 = 1.01.

-Dan