For this case we have that by definition, a linear function is of the form [tex]y = mx + b[/tex]
If we have that a and b are linear functions, then they are of the form:
[tex]a (x) = mx + b\\b (x) = nx + c[/tex]
If we multiply them we have: (Applying distributive property)
[tex](mx + b) (nx + c) = (m * n) x ^ 2 + mcx + bnx + bc = (mn) x ^ 2 + (mc + bn) x + bc[/tex]
That is, we get a quadratic function.
Answer:
[tex](ab) (x)[/tex]
