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Fourier transform and invese FT of signals

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I have attached some problems that I think I am working correctly. I wanted to verify the concept is correct.

A signal x(t) = exp(-t)*cos(3t) is turned on at t = 0. What is its Fourier transform?

Consider the signal in problem 6. What is the Fourier transform of its derivative with respect to time?

What is the Fourier transform of x = exp(-pi*16t^2)?

What is the inverse Fourier transform of X = cos(f)?

What is the inverse Fourier transform of X = cosh(f)?

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https://brainmass.com/engineering/electrical-engineering/fourier-transform-and-invese-ft-of-signals-189301

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Solution Summary

The solution shows how to calculate the Fourier transform of several signals using either definition or properties of FT. It also calculates the inverse Fourier transform of cosine and cosh(f).

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