Part CCSIR NET December 2023fredholm-alternative

Fredholm alternative

Consider the Fredholm integral equation $y (x) - 3 \int_{0}^{1} t x y (t)$ dt = f(x), with f continuous on [0, 1]. Which of the following choices for f(x) have the property that the equation admits at least one solution?

A. $f (x) = x^{2} - 1/2$
B.f(x) = eˣ
C.f(x) = 2 − 3x
D.f(x) = x − 1

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The trap it tests

Existence vs uniqueness

A theorem giving one was read as giving both.

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Fredholm alternative

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