## Task A-4.1.

Let $a, b$ and $c$ be real numbers and $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by

$$
f(x)=a x^{5}+b x^{3}+c \sin x-1
$$

If $f(-2015)=2015$, determine $f(2015)$.
## Solution.

Since $(-x)^{5}=-x^{5},(-x)^{3}=-x^{3}$ and $\sin (-x)=-\sin x$, we have

$$
f(-2015)=-2015^{5} a-2015^{3} b-c \sin 2015-1
$$

Therefore, $f(2015)=2015^{5} a+2015^{3} b+c \sin 2015-1=-f(-2015)-2=-2017$.