Question

One to one functions g and h are defined as follows.

g={ (-9,7), (-1,-6), (1,4), (6,-1)}
h(x)= 2x-9

Find the following of:
1.) g^-1 (-1) = ?
2.) h^-1 (x) =?
3.) (h o h^-1) (1)= ?

Answer 1

1. g^-1 ( - 1 ) = 6

2. h^-1 ( x ) = ?
y = 2 x - 9
- 2 x = - y - 9 / : ( -2 )
x = ( y + 9 )/ 2
h^-1 ( x ) = ( x + 9 ) / 2

3. ( h ° h^-1) ( 1 ) = ?
h ( h^-1 ( 1 ) )= h ( (1+9) /2 ) = h ( 5 ) = 2· 5 - 9 = 10 - 9 = 1