Note that in this question, as in most questions involving the decomposition of a function, *f *and *g* are not unique. Other possible choices for f and g might be

`f = 4 + x` and `g = 1/sqrt(x-5)`

or

`f = 4 + 1/x` and `g = sqrt(x-5)`

Both...

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Note that in this question, as in most questions involving the decomposition of a function, *f *and *g* are not unique. Other possible choices for f and g might be

`f = 4 + x` and `g = 1/sqrt(x-5)`

or

`f = 4 + 1/x` and `g = sqrt(x-5)`

Both of these pairs of *f *and *g *will result in the composition function

`f o g (x) = 4+1/sqrt(x-5)`

Here, we have to do the decomposition of the given function,

`h(x)= 4+1/sqrt(x-5)` into `f(x)` and `g(x)` such that `h(x)=(fog)(x)` .

In `(f o g)(x)` , `g(x)` is the inner function and `f(x)` is the outer function.

`g(x)` is to be plugged into `f(x)` to get `(fog)(x)` .

Hence, `g(x)= (x-5)` and

`f(x)=4+1/sqrtx`