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Forget about face recognition, James. The latest SPECTRE internet password requires you to combine functions in the innite dimensional vector space...

How can I solve this question?

I am very confusion about this questionScreen Shot 2018-08-06 at 12.39.40 pm.png

Screen Shot 2018-08-06 at 12.39.40 pm.png

Forget about face recognition, James. The latest SPECTRE internet password requires you to combine functions in the infinite dimensional vector space of functions to obtain
a “O-key" to crack into their evil web-portal. The pass key app here shows the functions ex .e‘x, cosh x, and sinhx together with the linear key combination f(x) = ae" + be—x + ccoshx +d sinhx.
Your mission, if you choose to accept it, is to find some combination of coefficients that will: i) ensure that the function
f(Jc) = aux +be_x + ccoshx+ d sinhx
is the zero function (or at least very close to it), and
ii) at least one of a, b, c, d is exactly equal to 1. Your solution James? Clearly the answer, or at least one answer, M, is given by the vector at b
c
d

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