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

question 28

Multiple Choice

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