CLASSIFICATION OF FUNCTION -
A.) Algebraic Functions –
A function which consists of a finite number of terms involving powers and roots of the independent variable x and the four fundamental operations of addition, subtraction, multiplication, and division is called an algebraic functions.
√(2x + 3)
Thus, 5x³- 7x²+ 6x + 2, (5x – 3)³, 3√(6x – 11), -----------
(x – 1)²
- are all algebraic functions.
Three particular cases of algebraic functions are –
(i) Polynomials or rational integral functions –
A function of the form a₀xᵉ + a₁xᵉ⁻¹+ a₂xᵉ⁻²+……….aₑ where f(x) is a positive integer and a₀, a₁, a₂,……aₑ are real constants is called a polynomial or rational integers function of x, e.g., 5x³- 6x²+ 4x – 2 is a polynomial.
(ii) Rational Function –
f(x)
A function of the form -------- g(x) ≠ 0, where f(x) and g(x) are
g(x)
polynomials in x is called a rational
5x²+ 6x – 2
function, e.g., --------------- is a rational functions.
x³+ x²+ 3
(iii) Irrational Functions –
The functions involving radicals are called irrational functions.
(x + 1)½ - (x – 3)½
e.g., √(5x²- 7x + 2), ----------------------
(5 + 3x)½ + (7 – 2x)⅔