Learn All Concepts of Chapter 2 Class 11 Relations and Function  FREE. Check  Relation and Function Class 11  All Concepts
We study addition, subtraction, multiplication and division in functions
Here the functions which we are taking are real functions
i.e. f: X → R
Where X is a subset of R and R is real numbers
Example
 f: R → R is a real function

f:
Z
→
R
is a real function
(Where Z is set of integers and integer is a subset of Real numbers i.e. Z ⊂ R )
Let f: R → R , g: R → R
f(x) = x, g(x) = x – 1
Addition
f + g = x + (x – 1) = 2x – 1
Subtraction
f – g = x – (x – 1) = x – x + 1 = 1
Multiplication by scalar
2f = 2 × f(x) = 2x
9g = 9 × g(x) = 9(x – 1) = 9x – 9
Multiplication
fg = x × (x – 1) = x ^{ 2 } – x
Division
f/g = x/(x  1)
Where x ∈ R and x – 1 ≠ 0
i.e. x ≠ 1
So, x will be all numbers except 1
So, x ∈ R – {1}
So, for f: X → R and g: X → R
(f + g) (x) = f(x) + g(x), x ∈ X
(f – g) (x) = f(x) + g(x), x ∈ X
(kf) (x) = k f(x), x ∈ X, k is a real number
(fg) (x) = f(x) × g(x), x ∈ X
(f/g) (x) = f(x)/g(x), x ∈ X, and g(x) ≠ 0