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# Evaluate the two compostions(fog)x and (hog)(x)   find the inverse...

tdt3 | eNoter

Posted May 31, 2013 at 12:26 AM via web

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Evaluate the two compostions(fog)x and (hog)(x)

find the inverse functions f^-1 (x) and h^-1( x)

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 2, 2013 at 12:56 PM (Answer #1)

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You need to compose two functions using the following relation, such that:

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

You should notice that the equation of second function `g(x)` replaces the variable x, in equation of function `f(x)` .

You may consider the following simple example, such that:

`f(x) = 3x - sin x`

`g(x) = sqrt x`

Using the equation `(fog)(x) = f(g(x))` , you can find the result of composition of function `f(x)` and `g(x)` , such that:

`f(g(x)) = 3g(x) - sin (g(x))`

Replacing `sqrt x` for `g(x)` yields:

`f(g(x)) = 3sqrt x - sin (sqrt x` )

Hence, you may evaluate the composition of any two functions, `f(x)` and `g(x)` , using the relation `(fog)(x) = f(g(x)).`

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