Inverse Of Function

If a relation or a function is given in the tabular form that is as a set of ordered pair, its inverse is obtained by interchanging the components of each ordered pair.inverse of function

The inverse of r and f are denoted by $inverse of r is denoted by$ and $\large f^{-1}$ respectively

If r and f are given in set tabular form, the inverse of each is obtained by interchanging x and y in the defining equation. The inverse of a function, which can be or may not be a function.

The inverse of a linear equation.

$inverse of linear function denoted by$

Which is also a linear function. RELATION FUNCTION

Briefly, we may say that the inverse of a line is linear.

SELF INVERSE OF FUNCTION

The figure line y=x is clearly show – self inverse.

IDENTITY FUNCTION : y =x or x = y

the function defined by the equation

$identity function$

EXAMPLE OF INVERSE OF FUNCTION:

Fined the inverse of

A: { (1,1), (2,4), (3,9), (4,16)………………x ∈ Z positive integers)

B: {( x,y) such that y= 2x+3, x belong to real number R)

SOLUTION:

The inverse is

{ (1,1), (2,4), (3,9), (4,16)………………}

this is also a function:

KEEP IN MIND

y= √ x, x ≥ 0 defines a function, but the equation y² = x , x ≥ 0 does not define a function.

SQUARE ROOT OF A FUNCTION:

The function defined by the equation

y = √ x , x ≥ 0 is called square root of a function.

EXAMPLE:

The equation y² = x

y = ± √ x

there the equation y² = x (x ≥ 0) may be shown as defining the union of the function defined by .

Y = √ x, x ≥ 0 and y = -√ x, x ≥ 0

LINEAR FUNCTION:

$\large \left \{ \left ( x,y \right )|\, y=2x+3 \right \}$

The given function is a linear function. Its inverse is

$linear function$

Which is also a linear function.

Point (0, 3), (-1.5, 0) lie on the given line and points (3,0), (0, -1.5) lie on its inverse.