convergence test for integral

[nazmi]

hey there.. i'm kinda lost here..
i need to do convergence test for the equation below...
$\displaystyle y(x)=\frac{1}{\sqrt{2\pi}}\frac{1}{a}\sqrt{\frac{\ pi}{a}}\int_{-\infty}^{\infty} e^{-a|x|}f(x-t)dt$

however.. i've got 2 value of f(x).. e^x^2 and x^5

how am i going to test them?
should i include my f(x) inside the equation above?
like this...
$\displaystyle y(x)=\int_{-\infty}^{\infty} e^{-a|x|}f(x-t)^{5}dt$

and..

$\displaystyle y(x)=\int_{-\infty}^{\infty} e^{-a|x|}f(e^{(x-t)^{2}})dt$

please guide me..

 

[daon]

Why are you plugging f(x) into f? The integral will of course depend on f, you've either not explained the problem adequately or you are not subbing into your integral correctly.