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given two functions, f(x), and g(x), explain how to determine algebraically if and g are inverses of each other. PLEASE SHOW ALL WORK, THANKS |

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Suppose that g is the inverse of f. Let's think for a moment about what this means. In order for this to be the case, it must be true that if for all x in the domain of f, if y = f(x), then x = g(y).

From this we see that then for all x, x = f(g(x)).

Therefore, to check algerbaically, you must confirm that x = f(g(x))

Example: `f(x) = 2x + 5, g(x) = (x - 5) / 2`

`f(g(x)) = 2 ( (x-5) / 2) + 5`

`= (x - 5) + 5`

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

Therefore we have confirmed that g is the inverse of f. This also implies that f is the inverse of g.

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