Answer
$f$ and $f^{-1}$ are inverses.
Work Step by Step
We are given the functions:
$f(x)=x+2$
$f^{-1}(x)=x-2$
Compute $f(f^{-1}(x))$ for $x\in\{-10,0,7,45\}$:
$f(f^{-1}(-10))=f(-12)=-10$
$f(f^{-1}(0))=f(-2)=0$
$f(f^{-1}(7))=f(5)=7$
$f(f^{-1}(45))=f(43)=45$
Compute $f^{-1}(f(x))$ for $x\in\{-10,0,7,45\}$:
$f^{-1}(f(-10))=f^{-1}(-8)=-10$
$f^{-1}(f(0))=f^{-1}(2)=0$
$f^{-1}(f(7))=f^{-1}(9)=7$
$f^{-1}(f(45))=f^{-1}(47)=45$
Put the data in a table.
We notice that we have:
$f(f^{-1}(x))=f^{-1}(f(x))=x$
This means the two functions are inverses of each other.
