The onetoone functions g and h are defined as follows g42104

The one-to-one functions g and h are defined as follows.

g={(-4,-2),(1,0),(4,1),(7,4)}

h(x)=3x-13

Find the following.

g^-1(4)=

h^-1(x)=

(h^-1 o h)(7)=

Solution

In case of one to one function : domain of original becomes range for invers and range of original function

becomes domain for inverse function.

So, g^-1(4) = 7

h(x) = 3x-13

y = 3x-13

h^-1(x) : relpce x =y and y=x and solve

x = 3y -13

3y = (x+13)

y = (x+13)/3

h^-1(x) = (x+13)/3

(h^-1 o h)(7) :

find (h^-1 o h)(x) : plug x= h(x) in h^-1(x)

(h^-1 o h)(x) = [ 3x -13 +13]/3 = x

(h^-1 o h)(7) = 7