Question

Question 2 of 10The one-to-one functions g and h are defined as follows.g={(-8, 6), (-6, 7), (-1, 1), (0, -8)}h(x)=3x-8Find the following.g-¹(-8)=h-¹(x) =(hoh− ¹)(-5) =

Answer 1

Answer: We have to find three unknown asked quantities, before we could do that we must find the g(x) from the coordinate points:

`\begin{gathered} g=\left\{\left(-8,6\right),(-6,7),(-1,1),(0,-8)\right\}\Rightarrow(x,y) \\ \\ \text{ Is a tabular function} \\ \end{gathered}`

The answers are as follows:

`\begin{gathered} g^(-1)(-8)=0\text{ }\Rightarrow\text{ Because: }(0,-8) \\ \\ \\ h^(-1)(x)=(x)/(3)+(8)/(3) \\ \\ \\ \text{ Because:} \\ \\ h(x)=3x-8\Rightarrow\text{ switch }x\text{ and x} \\ \\ x=3h-8 \\ \\ \\ \\ \text{ Solve for }h \\ \\ \\ h=h^(-1)(x)=(x)/(3)+(8)/(3) \end{gathered}`

The last answer is:

`\begin{gathered} (h\text{ }\circ\text{ }h^(-1))(-5) \\ \\ \text{ Can also be written as:} \\ \\ h[h^(-1)(x)]\text{ evaluated at -5} \\ \\ h(x)=3x-8 \\ \\ h^(-1)(x)=(x)/(3)+(8)/(3) \\ \\ \\ \therefore\Rightarrow \\ \\ \\ h[h^(-1)(x)]=3[(x)/(3)+(8)/(3)]-8=x+8-8=x \\ \\ \\ \\ h[h^(-1)(x)]=x \\ \\ \\ \\ h[h^(-1)(-5)]=-5 \end{gathered}`