The Solution of the Integral Equation $\int _ { 0 } ^ { - \infty } f ( x ) \cos ( a x ) d x = F ( \alpha )$

The solution of the integral equation $\int _ { 0 } ^ { - \infty } f ( x ) \cos ( a x ) d x = F ( \alpha )$ is

A) $f ( x ) = \int _ { 0 } ^ { \infty } F ( \alpha ) \cos ( \alpha x ) d \alpha / \pi$
B) $f ( x ) = 2 \int _ { 0 } ^ { \infty } F ( \alpha ) \cos ( \alpha x ) d \alpha / \pi$
C) $f ( x ) = 2 \int _ { 0 } ^ { \infty } F ( \alpha ) \cos ( \alpha x ) d \alpha$
D) $f ( x ) = \int _ { 0 } ^ { \infty } F ( \alpha ) \cos ( \alpha x ) d \alpha$
E) none of the above