Question

Given `f(x)=sqrtx` and `g(x)=x-1`, how do you determine the domain and range of `y=f(g(x))`?

Answer 1

Domain : `x>=1`. In interval notation `[1,oo)`
Range: `y>=0`. In interval notation `[0,oo)`

Explanation:

`f(x)=sqrtx ; g(x)=x-1 ; y=f(g(x))= ?`

Here Inside function is `g(x)=x-1`. Domain of inside function is any real number `x in RR` , Range: `g(x) in RR`

`y=f(g(x)) = f(x-1) = sqrt(x-1)` . Domain: under root should be `>=0 :. x-1>=0 or x>=1`.

Domain :`x>=1`.In interval notation `[1,oo)`

Range: `y>=0` In interval notation `[0,oo)`
graph{sqrt(x-1) [-10, 10, -5, 5]} [Ans]