I have Learnt
Cartesian product of any two non-empty sets A and B is a set containing all ordered pairs (x,y) such that x ∈ A and y ∈ B.
A function f from set A to set B is a relation, rule or mapping which maps each element of set A to a unique element of set B.
A function f: A→B will be into if range(f) ⊂ B.
A function f: A→B will be onto if range(f) ≡ B.
A function f: A→B will be one-one if unique element of A have unique image in B.
A function f: A→B will be injective if it is both into and one-one.
A function f: A→B will be bijective if it is both onto and one-one.
Every bijective function has one-one correspondence between its elements.
The process of finding the value of dependent variable by substituting any specific value of the independent variable is called evaluation of a function.
For any two functions f and g: (f+g)(x)=f(x)+g(x), (f-g)(x)=f(x)-g(x), (f×g)(x)=f(x)×g(x), (f÷g)(x)=f(x)÷g(x).
The composition of any two functions, f(x) and g(x) is denoted by (fog)(x) = f(g(x)).
If y=f(x) ∀x∈X, then x=f⁻¹(y) ∀y∈Y.
The domain of f(x) = range of f⁻¹(x) and range of f(x) = domain of f⁻¹(x).
A polynomial function of no degree is called a zero polynomial function.
A polynomial function of degree zero is called a constant function.
A polynomial function of degree one is called a linear function.
A polynomial function of degree two is called a quadratic function.