/sci/ - Science & Math

Can I have some help figuring what I'm doing wrong?

[math]x(t) = \frac{1}{1-i2\pi t}[/math]

Find F(x(t))

[math]x(t) = \frac{1}{1-i2\pi t} = - \frac{1}{-1+i2\pi t}[/math]

[math]F(x(t)) = F({\frac{1}{1-i2\pi t}}) = -F(\frac{1}{-1+i2 \pi t})[/math]
through linearity property
Using fourier pair
[math]e^{-at}u(t)\Leftrightarrow \frac{1}{a+i2 \pi f}[/math]

and duality property

[math]y(t) \Leftrightarrow Y(f)[/math]
[math]Y(t) \Leftrightarrow y(-f)[/math]

new fourier pair
[math]\frac{1}{a+i2 \pi t} \Leftrightarrow e^{-a(-f)} u(-f) = e^{af}u(-f)[/math]

therefore

[math] F(x(t)) = -F(\frac{1}{-1+i2 \pi t}) = -e^{(-1)f}u(-f) = -e^{-f}u(-f) [/math]

Yet wolfram and matlab don't give me the same answer. I have included what wolfram give's me as a picture