for the following functions f and g determine (a)f(g(x) (b)g(f(x) f(x)=3x+3 g(x)=-7x+7

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to compose the functions f(x) and g(x) such that:

a) (fog)(x) = f(g(x))

You need to substitute g(x) for x in equation of f(x) such that:

`f(g(x)) = 3g(x) + 3`

You need to substitute `-7x+7`  for g(x) in equation above such that:

`f(-7x+7) = 3(-7x+7) + 3`

`f(-7x+7) = -21x + 21 + 3 => f(-7x+7) = -21x + 24`

Hence, evaluating f(g(x)) yields `f(g(x)) = -21x + 24` .

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

You need to substitute f(x) for x in equation of g(x) such that:

`g(f(x)) = -7f(x) + 7`

You need to substitute `3x+3`  for f(x) in equation above such that:

`g(f(x)) = -7(3x+3) + 7 => g(f(x)) = -21x - 21 + 7`

`g(f(x)) = -21x - 14`

Hence, evaluating `g(f(x))`  yields `g(f(x)) = -21x - 14.`

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