The value of (fogoh)(x) is √x³ + 6x + 12√x
Here, we are given 3 functions:
f(x) = x³ +8
g(x) = x - 2
and, h(x) = √x
now, (fogoh)(x) can be written as-
f[g{h(x)}]
= f{g(√x)}
here, g(√x) = √x - 2
Thus,
f{g(√x)} = f(√x - 2)
Substituting x = √x - 2 in f(x) we get,
(√x - 2)³ +8
using (a + b)³ = a³ + b³ + 3ab(a + b), we get
= √x³ - 2³ + 3√x(-2){√x - 2} + 8
= √x³ - 8 + 6x + 12√x + 8
= √x³ + 6x + 12√x
Thus, the value of (fogoh)(x) = √x³ + 6x + 12√x
Learn more about composite functions here-
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