/jp/ - Otaku Culture

>>22042630
oh trial and error would be a nightmare. you use linear algebra instead
here's how it works, this'd be easier with pictures but i don't want to draw them right now

1.
there are three piecewise functions that define the sum. what you should notice is that it says polynomials but they are are only linear. we can thus assume the polynomials are only linear equations, so they're all in the form ax+b. so really we're solving for six numbers instead of an unknown amount, which is much nicer already

2.
there are three attributes to the piecewise, so we can assume they are non-horizontal lines that touch the x axis at different points. we know that one touches at -1 and the other touches at 0 because of the piecewise conditions

3.
you can set up two systems of linear equations to solve for the values of a and b for all three functions. augmented matrix, gaussian elimination gives you two possible answers (since we don't know enough to single it down yet) and you can check at x=0 which one of the answers is correct (the other's b values don't check out). with the values you can then put them in and show they work