Question

Create a table of values for the function and inverse relation

Answer 1

First, let us create a table for:

`\begin{gathered} f(x)=x^2+1 \\ (-3\leq x\leq3) \end{gathered}`

The table of values:

The Inverse:

`\begin{gathered} y=x^2+1 \\ x^2=y-1 \\ x=√(y-1) \\ f^(-1)(x)=√(x-1) \end{gathered}`

For the values with inverses:

`\begin{gathered} f^(-1)(x)=√(x-1) \\ (-3\leq x\leq3) \end{gathered}`
`\begin{gathered} f^(-1)(-3)=√((-3)^2-1)=√(9-1)=√(8) \\ f^(-1)(-2)=√((-2)^2-1)=√(4-1)=√(3) \\ f^(-1)(-1)=√((-1)^2-1)=√(1-1)=√(0)=0 \\ f^(-1)(0)=√((0)^2-1)=√(0-1)=√(-)1(discontinues) \\ f^(-1)(1)=√((1)^2-1)=√(1-1)=√(0)=0 \\ f^(-1)(2)=√((2)^2-1)=√(4-1)=√(3) \\ f^(-1)(3)=√((3)^2-1)=√(9-1)=√(8) \end{gathered}`

The table of values for the inverse: