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Foundation for functions – Algebra Lesson (Mathematics )


What is a Function?

A function can be expressed in many ways, some of them being linear, quadratic, logarithmic functions etc. But just like numbers there are operations which can be used even on functions.

Addition and Subtraction between functions:

Foundation for functions


If f(x) = 2x+3 and g(x) = 3x+5, then find (f+g)(x) and (f –g)(x).

So, by using the above formula,

(f+g)(x) = 2x+3+3x+5    Combine like terms!

è(f+g)(x) = 5x+8

(f –g)(x) = 2x+ 3 – (3x+5) è 2x+3 – 3x-5

è(f-g)(x) = -x-2

Multiplication and Division of functions:

Type of functions


If f(x) = (x2+ 4), g(x) = (2x+8), find (f.g)(1), (f/g)(1).

So, (f.g)(1) = f(1).g(1)

f(1)=(12+ 4)= 5 and g(1)= 2(1)+ 8= 10

è(f.g)(1)= 5.10 = 50

è(f/g)(1)= f(1) / g(1) = 10/50= 1/2

Composition between functions:

Example: f(x)= 2x+3, g(x)= 3x+5, find fog(x)

fog(x)= f(g(x))

f(3x+5)= 2(3x+5) +3

-> 6x+10+3  -> 6x+13 = fog(x)

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