#### description

- Sum, Difference,Product and Quotient of Function
- Addition of two real functions
- Subtraction of a real function from another
- Multiplication by a scalar
- Multiplication of two real functions
- Quotient of two real functions

#### notes

Here, we shall learn how to add two real functions, subtract a real function from another, multiply a real function by a scalar (here by a scalar we mean a real number), multiply two real functions and divide one real function by another.**(i) Addition of two real functions****:** Let f : X → R and g : X → R be any two real functions, where X ⊂ R. Then, we define (f + g): X → R by

(f + g) (x) = f (x) + g (x), for all x ∈ X.

Example- `f(x)= x^2+1 and g(x)= sqrt(x-1)`

`(f+g)(x)= x^2+1+ sqrt(x-1)`**(ii) Subtraction of a real function :** from another Let f : X → R and g: X → R be any two real functions, where X⊂ R. Then, we define (f – g) : X→R by (f–g) (x) = f(x) –g(x), for all x ∈ X.

Example- `f(x)= x^2+1 and g(x)= sqrt(x-1)`

`(f-g)(x)= x^2+1- sqrt(x-1)`**(iii) Multiplication by a scalar :** Let f : X→R be a real valued function and α be a scalar. Here by scalar, we mean a real number. Then the product α f is a function from X to R defined by (α f ) (x) = α f (x), x ∈X. (kf)(x)= kf(x), where k is a constant.

Example 1- `f(x)= x^2+1 and g(x)= sqrt(x-1)`

`(fg)(x)= (x^2+1)[sqrt(x-1)]`

Example 2- `f(x)= x^2+1`

`3f(x)= 3(x^2+1)`**(iv) Quotient of two real functions :** Let f and g be two real functions defined from

X→R, where X⊂R. The quotient of f by g denoted by f/g is is a function defined by, `(f/g)(x)=[f(x)]/[g(x)]`, provided g(x) ≠ 0, x ∈ X.