Show that the following pairs of sets S and T are equinumerous by finding a specific bijection between the two sets in each pair.
a. S= [0,1] and T = [1,3]
b. S= [0,1] and T = [0, infinity]
Think geometrically. Length of $\displaystyle [0,1]$ is $\displaystyle 1$ and length of $\displaystyle [1,3]$ is $\displaystyle 2$. Thus, strech $\displaystyle [0,1]$ to $\displaystyle [0,2]$. Now shift this interval by one to the right this gives $\displaystyle [1,3]$.
Now the streching can be desribed by function $\displaystyle f :[0,1] \to [0,2]$ by $\displaystyle f(x) = 2x$. And the shifting can be described by $\displaystyle g:[0,2]\to [1,3]$ by $\displaystyle g(x) = x+1$. Thus, $\displaystyle g\circ f: [0,1] \to [1,3]$ is what you are looking for. Finally $\displaystyle g(f(x)) = 2x+1$ is the mapping you want.