# 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:**

**Example:**

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:**

**Example:**

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

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

f(1)=(1^{2}+ 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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