Question

Please solve this question!

Answer 1

Notice that for each function, they are simply in the form
`f(k(x))`, where
`k(x)` is some function of
`x.` More specifically,
`g(x)=f(x-2), h(x)=f(2x), \text{ and } j(x) = f(x^2).`

Thus, because the Interval of Convergence of
`f(x)` is
`-3 < x < 3,` the Interval of Convergence of
`g(x)` should be
`-3 < x-2 < 3 \implies -1 < x < 5.`

Similarly, the Interval of Convergence of
`h(x)` is
`-3 < 2x < 3 \implies -\frac32 < x < \frac32.`

Finally, the Interval of Convergence of
`j(x)` should be
`-3 < x^2 < 3 \implies 0 < x < √(3).`