college algebra functions

Introduction to college algebra functions:

Algebra is the branch of mathematics that satisfies operations' properties and the structures which these operations are defined. A function is nothing but a relation between each input number and one output number. Algebra functions include exponential function, log function, Quadratic functions, Even and Odd functions. Let us learn some concepts and example problems in algebra functions.

 

college algebra functions-Concepts in Algebra Functions:

 

Exponential function:

The function f given by f(x) = b x , where b > 0, b `!=` 1, and the exponent x is any  real number, is called an exponential function.

Log Function:

The logarithmic function that contain base b, where b > 0 and b `!=` 1, is given by logb and is defined by y = logb x, if and only if by = x

 

Quadratic functions:

It is a polynomial of highest power two. The basic function is: F(X) = ax2 + bx + c. Here ax2 is quadratic term, bx is linear term and c is constant. The letters a and b are coefficients.

Even functions:

The function is called even if the graph is symmetric to y-axis, in other words f(x) = f(- x).

Odd functions:

The function is called odd if the graph is symmetric to origin, in other words f(-x) = - f(x).

college algebra functions-Example Problems:

Sum of functions:

(f + g)(x) = f(x) + g(x)

Example 1:

               If f(x) = 4x + 1 and g(x) = x + 2 then find (f + g)(x)

               Solution:

                    (f + g)(x) = (4x + 1) + (x + 2)

                                  = 4x + 1 + x + 2

                                  = 5x + 3

Product of functions:
(fg)(x) = f(x)g(x)

 

Example 2:

               If f(x) = 4x + 1 and g(x) = x + 2 then find (fg)(x)

              Solution:

                  (fg)(x) = (4x + 1)(x + 2)

                            = 4x2 + 8x + x + 2

                            = 4x2 + 9x + 2