I have two Fourier transforms to solve, but the problem is that a I have a characteristic bijection or some etching that I don't know what it is and I don't know how to solve this... Please help
$$f(x)=e^{-x}\chi_{[0,\alpha]}(x)$$
$$g=(1-|x|)\chi_{[-1,1]}(x)$$
For any function $f$, the Fourier Transform of $f$ is $$ \mathscr{F}f(\xi)=\int_{-\infty}^\infty f(x)\,e^{-2\pi ix\xi}\,\mathrm{d}x $$ and $$ \chi_{[a,b]}(x)=\left\{\begin{array}{} 1&\quad\text{if }a\le x\le b\\ 0&\quad\text{otherwise} \end{array}\right. $$ Thus, for the functions in your question, $$ \mathscr{F}f(\xi)=\int_0^\alpha e^{-x}\,e^{-2\pi ix\xi}\,\mathrm{d}x $$ and $$ \mathscr{F}g(\xi)=\int_{-1}^1(1-|x|)\,e^{-2\pi ix\xi}\,\mathrm{d}x $$