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Find (g circle f)(-4) f(x) = -x squared + 4 g(x) = 2x

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted February 18, 2013 at 5:14 AM via web

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Find (g circle f)(-4)

f(x) = -x squared + 4

g(x) = 2x

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted February 18, 2013 at 8:02 AM (Answer #1)

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You need to evaluate the composition of the function f(x) and g(x), such that:

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

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

`f(g(x)) = -(g(x))^2 +4`

Substituting `2x` for `g(x)` yields:

`f(g(x)) = -(2x)^2 + 4 => f(g(x)) = -4x^2 + 4`

You need to evaluate `f(g(x))` at `x = -4` , such that:

`f(g(-4)) = -4(-4)^2 + 4 => f(g(-4)) = -64 + 4 = -60`

Hence, evaluating `f(g(-4))` , under the given conditions, yields `f(g(-4)) = -60` .

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