Question

Find the domain and range of the following real functions:

(i) f(x) = - |x|

(ii) f(x) = √(9 - x²)

(iii) f(x) = √(x - 1)

(iv) f(x) = |x - 1|

Answer 1

Remark: Operations of functions:

(i) Addition of two real functions:

Let f: X → R and g : X → R Then.

(f + g):X → R; (f + g)(x) = f(x) + g(x) for all x ∈ X 

(ii) Difference of two real functions: 

Let f : X → R and g : X → R Then. 

(f – g): X → R; (f- g)(x) = f(x) – g(x) for all x ∈ X 

(iii) Scalar multiplication of a function: 

Let f: X → R and let ‘a’ he a scalar. Then, 

(αf):X → R; (fg)(x) = f(x) for all x ∈ X 

(iv) Multiplication of two real functions: 

Let f: X → R and g : X → R .Then 

(fg): X → R; (fg)(x)= f(x)g(x), for all x ∈ X 

(v) Quotient of two real functions: 

Let f: X → R and g : X → R for all x for which g(x) ≠ 0. Then

(f/g) : x → R : (f/g) (x) = f(x)/g(x)