one to one functions

Question

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

 

g= {(0,6),(4,-3),(6,0),(8,5)}

 

h(x)=3x-4

 

Find the following.

 

g^-1 (6) = ?

 

h^-1 (x) = ?

 

(h o h^-1)(2) = ?

Answer 1

g= {(0,6),(4,-3),(6,0),(8,5)}  &  h(x)=3x-4


g^-1 (6) = 0 by interchanging x & y from the first given pair in the definition of g

h^-1 (x) = (x+4)/3 by the usual process of interchanging letters x & y & then solving for y, which is inverse of h.

(h o h^-1)(2) = 2 because, by definition, f(f^-1(x)) = x for any function having an inverse.