It lists one to one functions:
$g=\{(-5,-3),(2,5),(3,-9),(8,3)\}$
$h(x)= 3x-2$
And it asks to find the following:
$g^{-1} (3) = h^{-1}(x)= (h * h^{-1})(-5)=$
I really need help with this problem, I especially don’t get what g does. Does it multiply all the coordinates by 3? Please help
The inverse of a function is an equation for which f(y)=x. That means, for every point (x,y) on the original function, there is a point (y,x) on the inverse. This means that $g(x)=g^{-1}(y)$, for any (x,y) pair on g(x). So, the value of $g^{-1}(3)$ is asking for what value of x is y equal to 3, the converse of $g(3)$, which is asking for what value of y is x equal to 3. For sets like g(x), that means looking through and finding pairs in the form (x,3). For equations like h(x), replace the x with y, and the y with x, and isolate the new y in the new equation. That equation is then the equation of the inverse. Then, you can evaluate that equation normally to find various values of $g^{-1}(x)$.