Question

Let `f(X)=e^(x),R^(+)toR` and `g(x)=sinx,[-(pi)/2,(pi)/2]to[-1,1]` Find domain and range of `fog(X)`

Answer 1

Domain of `f(x):(0,oo)` Range of `g(x):[-1,1]`
values in range of `g(x)` which are accepted by `f(x)` are `(0,(pi)/2]`
`implies0ltg(x)le1implies0ltsinleimplies0ltxle(pi)/2`
Hence domain of `fog(x)` is `xepsilon(0,(pi)/2]`
Therefore Domain : `(0,(pi)/2]`
Range : `(1,e]`