VIDIO INVERS FUNCTION

The Inverse of a function

Definition: The inverse of the function is when the domain and the range trade places. All elements of the domain become the range, and all elements of the range become a domain.

Example of the inverse of a simple function

Original function f(x)	Inverse of function or f-1(x)
{ (0,3 ) , (1,4) , (2, 5) }	{ (3, 0 ) , (4,1) , (5, 2) }

Function invers to shape the function is “invers function”. Invers function of f can written f^-1 (read invers function f).

Given a function , its inverse is defined by

Therefore, and are reflections about the line . In Mathematica, inverse functions are represented using InverseFunction[f].

Example :

v y = 2x – 1

if y = 0 so

0 = 2x – 1

x = 1/2 so coordinat’s (1/2,0)

if x = 0 so

y = 0- 1

y = -1 coordinat’s (0,-1)

v x = 2x -1

1 + x = 2x

1 = x

v y = 2x -1

2x = y + 1

x = ½ (y + 1)

x = ½ y + ½

· function f and function g can combination with a rule to be certain, and a rule this as some function composition

· function composition f continued function g(given sign g0f)

example :

let f(x) = 2x – 1

g(x) = 1/2x + ½

determine fog and gof

solution :

· (fog) = f (g(x))

= 2(1/2x + ½) – 1

= x + 1 – 1

= x

· (gof) = g(f(x))

= ½(2x-1) + ½

= x – ½ + ½

= x