Question

What is the value of f[g(4)] for the functions f(x) = 2x + 1 and g(x) = 2x - 5? (Type only the value of your final answer, no variables.)

Answer 1

\[f(x) \approx \sum_{n=0}^{∞}_{n \in Z}c_n e^{\frac{ i n \pi }{ L }}\]
\[c_n = \frac{ 1 }{ 2 \pi } \int\limits_{-\pi}^{\pi}f(x)e^{- i n x}dx\]
if n = 0, then
\[c_0 = \frac{ 1 }{ 2\pi } \int\limits_{-\pi}^{\pi} x^2dx = \frac{ 1 }{ 2\pi }\frac{ x^3 }{ 3 }\]
evaluated from -π < x < π to give:
\[\frac{ \pi^2 }{ 3 }\]
when n≠0
use parts to integrate twice and get
\[c_n = \frac{ 2(-1)^n }{ n^2 }\]

Answer 2

thank u