Find pattern of function with 2 inputs

Question

Given:

$1*2=7$

$2*(-4)=2$

$(-7)*3=12$

Find: $[(-3) * 1]*(-5)$

There must be some function $f(a,b)$ related to $a*b$ but i couldn't find that out.

Answer 1

One answer can be of the form $ma+nb+kab$. So solving for the above three equations one gets $f(a,b) = 2.907692a + 3.138462b - 1.092308ab$. Putting this relation for $[(-3)*1]*(-5)$ one gets the answer $-35.0059$.

Since there are three relations for this $*$ operator by adding a known function of $g(a,b)$ we can create a function of the form $ ma+nb+k.g(a,b)$ and solve for $(m,n,k)$. If there is no constraint on the type of solution e.g. integer numbers, then we can get infinite number of such relations.