Operations on Functions and Inverse of a Function
Evaluating a Function
A function is usually written as y = f(x), in which the values of y (dependent variable) depends upon the values of x (independent variable) and is read as 'y is a function of x or simply y is equal to f of x'.
Evaluation of a function is a process of finding the value of dependent variable by substituting any specific value of the independent variable.
Example: Find the value of f(x) = -2x³ + x² at:
(I) f(-1) (II) f(t) (III) f(-1/2) (IV) f(x+2)
Solution: (I) f(-1) = -2(-1)³ + (-1)² = -2(-1) + 1 = 3
(II) f(t) = -2t³ + t²
(III) f(-1/2) = -2(-1/2)³ + (-1/2)² = 1/4 + 1/4 = 1/2
(IV) f(x+2) = -2(x+2)³ + (x+2)² = -2x³ - 11x² - 20x - 12
Operations on Functions
Operations on functions are the ways of combining functions to create new functions. Some common operations on any two functions f(x) and g(x) are:
(i) Addition: (f+g)(x) = f(x) + g(x)
(ii) Subtraction: (f-g)(x) = f(x) - g(x)
(iii) Multiplication: (f×g)(x) = f(x) × g(x)
(iv) Division: (f÷g)(x) = f(x) ÷ g(x), where g(x) ≠ 0