Question

The one-to-one functions g and h are defined as follows.g={(-8, 2), (-5, 6), (4, -8), (9, -9)}h(x) = 9x+13Find the following h^-1(-8)=h^-1(x)=(h^-1•h)(-2)

Answer 1

Given

g={(-8, 2), (-5, 6), (4, -8), (9, -9)}

h(x) = 9x+13

Then for g^-1(-8):

`\begin{gathered} given\text{ g(}4)=-8 \\ g^(-1)(-8)=4 \end{gathered}`

for h^-1(x):

`\begin{gathered} h(x)=9x+13 \\ \text{change h(x) to y} \\ y=9x+13 \\ i\text{nterchange x and y} \\ x=9y+13 \\ \end{gathered}`

And solve for y:

`\begin{gathered} x-13=9y+13-13 \\ x-13=9y \\ (x-13)/(9)=(9y)/(9) \\ y=(x-13)/(9) \\ \text{change y to }h^(-1)(x) \\ h^(-1)(x)=(x-13)/(9) \end{gathered}`

for (h^-1 o h)(-2):

`(h^(-1)o\text{ h})(-2)=h^(-1)(h(-2))`

So,

`\begin{gathered} h^(-1)(9(-2)+13)=h^(-1)(-18+13)=h^(-1)(-5)=(-5-13)/(9)=(-18)/(9)=-2 \\ \end{gathered}`

Answer:

`\begin{gathered} g^(-1)(-8)=4 \\ h^(-1)(x)=(x-13)/(9) \\ (h^(-1)o\text{ h)(-2)=}-2 \end{gathered}`