The onetoone functions g and h are defined as follows g9 17

The one-to-one functions g and h are defined as follows. g={(-9, 1),(-7, 8),(1, -9). (8, 6)} h(x) = x+2/7 Find the following. G^-1(8) = h^-1(x) = (h degree h^-1)(0) =

Solution

a) g^-1 (8 ) = -7

b) h(x) = ( x+ 2) / 7

let y = ( x+ 2) / 7

to find inverse of h(x) , switch x and y and solve for y

x = (y+2) / 7

multiplying both sides by 7

7x = y + 2

y = 7x - 2

therefore, h^-1 (x) = 7x - 2

c) ( h o h^-1 ) (0)

first find ( h o h^-1 )(x)

( 7x-2+ 2) / 7 = x

hence , ( h o h^-1 )(0 ) = 0