g5 7 3 8 7 6 8 7 hx 4x13 Find the following g17 h1x The on

g={(?5, 7), (?3, 8), ?(7, 6), (?8, 7)}

h(x) =4x+13

Find the following.

g^-1(7) =

h^-1(x) =

Solution

.To find the domain and range of the inverse, just swap the domain and range from the original function

The given function is not one-to-one function as A one-to-one function, is a function in which for every x there is exactly one y and for every y, there is exactly one x.

Here g = (-5,7) and ( -8,7) both have y\'s so inverse g^-1(7) does not exist.

h^-1(x)

h(x) =y= 4x +13 .Plug y=x and x=y in h(x) to find h^-1(x)

y= 4x +13;

x = 4y +13

4y = x-13

y = (x- 13)/4 =h^-1(x)

(h o h) ;Plug h(x) =x in h(x)

=4(4x+13) +13 = 16x + 52 +13= 16x + 65

(h o h) ^-1(x):

y= 16x +65

x = 16y +65

y = (x -65)/16 = (h o h) ^-1(x)

(h o h) ^-1(1) = ( 1- 65)/16 = -64/16 = -4