Question

The graph of the invertible function
\[g\] is shown on the grid below.
A coordinate plane. The x- and y-axes each scale by one. The graph of y equals g of x is a continuous nonlinear curve that starts near negative six, negative ten and rapidly increases through the point negative five, negative four and the point negative four, one. It continues to increase to near negative three, three where the graph increases much slower through negative two, three. Then it increases rapidly again through the point zero, five and the point one, ten.
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{7}\]
\[\small{8}\]
\[\small{9}\]
\[\small{\llap{-}2}\]
\[\small{\llap{-}3}\]
\[\small{\llap{-}4}\]
\[\small{\llap{-}5}\]
\[\small{\llap{-}6}\]
\[\small{\llap{-}7}\]
\[\small{\llap{-}8}\]
\[\small{\llap{-}9}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{7}\]
\[\small{8}\]
\[\small{9}\]
\[\small{\llap{-}2}\]
\[\small{\llap{-}3}\]
\[\small{\llap{-}4}\]
\[\small{\llap{-}5}\]
\[\small{\llap{-}6}\]
\[\small{\llap{-}7}\]
\[\small{\llap{-}8}\]
\[\small{\llap{-}9}\]
\[y\]
\[x\]
\[y=g(x)\]
What is the value of
\[g^{-1}(1)\]?

Answer 1

g^{-1}(1) is the x with g(x)=1. The graph shows g(-4)=1, so g^{-1}(1) = -4.