Invertible Functions
Functions of Class 11
Invertible Functions
Let f : A→B be a one one and onto function then there exists a unique function g : B→A.
Such that f(x) = y ⇒ g(y) = x = f -1(y), ∀ x ∈ A and y ∈ B.
Then g is said to be the inverse of f.
And fo f -1 = f -1o f = I (an identify function)
and fo f -1 (x) = f -1o f (x) = I(x) = x
⇒ f {f -1 (x)}= x.
Note: If f is one to one then f has an inverse and conversely if f has an inverse then f is one to one from A to B and g is one to one from B to C then fo g is one to one from A to C and (fo g)-1 = g-1o f -1.
- Introduction
- Algebraic Operations On Functions
- Type of Functions
- Composition of functions
- Invertible Functions
- Domain and Range of Inverse Trigonometric Functions
- Odd And Even Functions
- Periodic Functions
- Methods to Find Period of A Periodic Function
- Signum Function
- Greatest Integer Function
- Modulus Function or Absolute Value Function
- Rational And Irrational Function
- Algebraic And Transcendental Function
- Explicit Function
- Exercise 1
- Exercise 3(Subjective)
