Question

The relation f is defined by `f(x)={x^2,0lt=xlt=3 3x ,3lt=xlt=10`The relating g is defined by `g(x)={x^2,0lt=xlt=3 3x ,2lt=xlt=10`Show that f is a function and g is not a function.

Answer 1

We have, dom `(g)=[0,10]subR`. It is easy to verify that every element in [0,10] is associated with a unique real number under g.
In particular `g(3)=3^(2)=9` and also `g(3)=3xx3=9`, i.e., 3 has a unique image, namely 9.
`:.` g is a function from [0,10] into R.