Let `R^+` be the set of all non-negative real numbers. if `f: R^+ rarrR^+` and `g: R^+rarrR^+` are defined as `f(x)=x^2` and `g(x)=+sqrt(x)dot` Find `fog` and `gofdot` Are they equal functions.

Explanation

`f circ g` means `g(x)` function is in `f(x)` function.


`g circ f` means `f(x)` function is in `g(x)` function.


`f: R^{+} rightarrow R^{+}`and `g: R^{+} rightarrow R^{+}`


So, `{f} circ {g}: {R}^{+} rightarrow {R}^{+}`and `{g} circ rightarrow {R}^{+}`


Domains of `f circ g` and `g circ f` are the same.



`Rightarrow {f} circ {g}({x}) ={f}[{g}({x})]`


`={f}(sqrt{{x}}) ldots ldots ldots[text { Since, } {g}({x})=sqrt{{x}}]`


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