So this is taken from my textbook, but I cant seem to understand why is it so.
"When the Maclaurin series for a function f(x) is known, we can substitute $kx$ (where $k$ is a constant) for $x$ to obtain the series for $f(kx)$. This may not be applicable to the other forms such as $f(k+x)$ for practical reasons."
If you know that the Maclaurin series for $f(x)$ is given by the sequence $(a_i)$, that is, $$ f(x) = \sum_{i=0}^n a_ix^i, $$ then we have that $$ f(kx) = \sum_{i=0}^n a_i k^i x^i. $$ So by setting $b_i = k^i a_i$, we have that the Maclaurin series for $f(x)$ is given by $(b_i)$. This is simple. However, looking at $f(x + k)$, we get $$ f(x+k) = \sum_{i=0}^n a_i(x + k)^i = \sum_{i=0}^\infty a_i\sum_{j=0}^i\binom{i}{j} x^jk^{i-j} = \sum_{i = 0}^\infty \left(\sum_{l=0}^\infty\binom{i+l}{i}a_{i+l}k^l\right)x^i. $$ So now the coefficients are given by $$ c_i = \sum_{l=0}^\infty\binom{i+l}{i}a_{i+l}k^l, $$ and it's not even obvious if and when these series converge, never mind what value they have.