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Watz · Answer 1 · 2023-04-26T23:29:32+0000

SOLUTION:

First, let us create a table for:

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

$\begin{gathered} f(-3)=(-3)^2+1\Rightarrow9+1=10 \\ f(-2)=(-2)^2+1\operatorname{\Rightarrow}4+1=5 \\ f(-1)=(-1)^2+1\operatorname{\Rightarrow}1+1=2 \\ f(0)=(0)^2+1\operatorname{\Rightarrow}0+1=1 \\ f(1)=(1)^2+1\operatorname{\Rightarrow}1+1=2 \\ f(2)=(2)^2+1\operatorname{\Rightarrow}4+1=5 \\ f(3)=(3)^2+1\operatorname{\Rightarrow}9+1=10 \end{gathered}$

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:

Create a table of values for the function and inverse relation-example-1

Create a table of values for the function and inverse relation-example-2

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