# Evaluate Mathematical Functions

Evaluate real valued functions: A step by step tutorial, with examples and detailed solutions. To find the value f(a) of a function, a has to be in the domain of f. In what follows, we are considering only real valued functions.

 Example 1: Evaluate, if possible, f(-2) and f(2) given that f is defined by f (x) = - 4 / ( x + 2) Solution to Example 1 Function f given above has domain (- infinity , - 2) U (- 2 , + infinity) Since at x = - 2 the denominator of f(x) is equal to 0, f(-2) = undefined. To find f(2), substitute x by 2 in f(x) = -4 / ( x + 2) f(2) = - 4 / (2 + 2) = -1. Example 2: Evaluate, if possible, g(3) and g(0) given that g is defined by g (x) = √(x - 3) Solution to Example 2 To find g(3), substitute x by 3 in the formula of the function g (3) = √(3 - 3) = √(0) = 0 The domain of g is given by the interval [3 , +infinity) x = 0 is not included in the domain, hence g(0) = √(0 - 3) = √(-3) = not a real number. Example 3: Evaluate, if possible, h(4), g(4) and h(4) / g(4) where functions h and g are defined by h (x) = 3x - 8 , g (x) = x 2 - 16 Solution to Example 3Evaluate h(4) h(4) = 3(4) - 8 = 4 Evaluate g(4) g (4) = 4 2 - 16 = 16 -16 = 0 In evaluating h(4) / g(4), g(4) which is the denominator is equal to 0. In mathematics division by zero is not allowed. Hence h(4) / g(4) = undefined Example 4: Evaluate, if possible, h(t -1) where function h is defined by h (x) = 2 x 2 - 2 x + 2 Solution to Example 4 The domain of this function is the set of all real numbers. Hence h(t -1) is given by h (t - 1) = 2 (t - 1) 2 - 2 (t - 1) + 2 Expand the square and group like terms h (t - 1) = 2 (t 2 - 2t + 1) - 2t + 2 + 2 = 2t 2 - 4t + 2 - 2t + 4 = 2t 2 - 6t + 6 Exercises: 1 - Evaluate f(9) given that f(x) = 2 x 2 + 2 2 - Evaluate g(1), h(1) and g(1) / h(1) given that g(x) = x 3 + 1 and h(x) = x - 1 3 - Evaluate f(t + 2) given that f(x) = - 2 x 2 + 2x Solutions to Above Exercises: 1 - f(9) = 164 2 - g(1) = 2 , h(1) = 0 , g(1) / h(1) = undefined 3 - f(t + 2) = - 2 t 2 - 6t - 4 More mathematics tutorials and problems are presented in this site.