Consider the following Fredholm integral equation
\(y(x)-3 \displaystyle \int_0^1 t x y(t) d t=f(x)\)),
where f(x) is a continuous function defined on the interval [0, 1]. Which of the following choices for f(x) have the property that the above integral equation admits at least one solution?
1
\(f(x)=x^2-\frac{1}{2}\)
2
f(x) = ex
3
f(x) = 2 - 3x
4
f(x) = x - 1