Question

The one-to-one functions g and h are defined as follows.
g={(-6,3),(3,-8),(5,-9),(7,-6)}
h(x)=3x-2
Find The Following:

g^-1 (3) =
h^-1 (x) =
(h o h) ^-1 (1) =

Answer 1

since \[g(-6)=3\] you get \[g^{-1}(3)=-6\]

Answer 2

second one solve \[3x-2=y\] for x to get \[x=\frac{y+2}{3}\]

Answer 3

then write \[h^{-1}(x)=\frac{x+2}{3}\]

Answer 4

now you know that \[h^{-1}(x) = \frac{x+2}{3}\] so \[h^{-1}(1)=\frac{1+2}{3}=1\]
and therefore \[h^{-1}(h^{-1}(1))=h^{-1}(1)=1\]