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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the values of resulting functions, `fog` and `gof,` using the definition of composition of two functions, such that:

`(fog)(x) = f(g(x))`

You need to notice that the variable x of the function is replaced by the value of function `g(x) = y` , hence, you need to collect all y coordinates of the function g(x), such that:

`g(x) = y = {-8,-2,0,3,5,6,9}`

Replacing each value of `g(x)` in equation `f(g(x))` yields that the domain of the function f(x) does not contain the value `x = -8.`

`(gof)(x) = g(f(x))`

`f(x) = y = {-5,-1,0,2,3,6,8}`

Replacing each value of `f(x)` in equation` g(f(x))` yields that the domain of the function g(x) does not contain the value `x = -5` .

Hence, since the domain of the functions `f(x)` contains values that there are not found in the range of `g(x)` and the range of the functions `f(x)` contains values that there are not found in the domain of `g(x)` , the composition of the functions `(fog)(x)` and  `(gof)(x)` cannot be evaluated.

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