Given f(x) = x^2 + 4 and g(x) = sqrt (x – 4), what is fog(3)?
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We are given the functions f(x) = x^2 + 4 and g(x) = sqrt(x- 4)
fog(x) = f (g(x)) = f (sqrt (x- 4))
=> (sqrt (x – 4)) ^2 + 4
=> (x – 4) + 4
=> x
Therefore fog (3) = 3.
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We'll write the composition of the functions first:
(fog)(x) = f(g(x))
We'll substitute x by g(x):
f(g(x)) = g(x)^2 + 4
f(g(x)) = [sqrt (x – 4)]^2 + 4
f(g(x)) = x - 4 + 4
We'll eliminate like terms:
f(g(x)) = x
So, f(g(3)) = 3.
Given f(x) = x^2 + 4 and g(x) = sqrt (x – 4), To find fog(3).
f(x) = x^2+4.
To find fog(x) we substitute g(x) in place of x in f(x) = x^2+4.
Therefore fog(x) = {sqrt(x-4)}^2+4
fog(x) =x-4+4 = x.
fog(x) = x.
fog(3) = 3.
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