Inverse Functions: Linear, discrete

Question

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

g= {(-6,-3), (0,9), (3,0), (6,4), (7,1)}

h(x)= 3x +10 

 

Find the following.

g^-1 (0) = ____

h^-1(x) =____

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

 

Thank you so much! I truly appreciate it! :D 

Answer 1

for (a,b) as any point in function g, then (b,a) is the corresponding point on the inverse of g so your first answer is 3.

 

you should be able to determine the formula for h inverse by the usual procedure given in all algebra books:

1) interchange x & y  (2)  solve for the new y   (3) relabel this result as y  --- where y values are always understood to be h values, when the function in question is named h.

 

the third answer is 1 because, by definition, h(h^-1(x) = x. that is, the successive operation of h and h inverse 'wipe out each other', leaving just the argument.