Let A={x∈R | -1≤x≤1} and let f:A→A, g:A→A be two functions defined by f(x)=x2 and g(x)=sinπx2. Show that the inverse of g exists but the inverse of f does not exist. Also, find the inverse of g.

Let $A = {x \in R | - 1 \leq x \leq 1}$ and let $f : A \to A, g : A \to A$ be two functions defined by f(x)= $x^{2}$ and g(x)= $\sin \frac{πx}{2}$ . Show that the inverse of g exists but the inverse of f does not exist. Also, find the inverse of g.

Match the items on the right to the items on the left.