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If ​f(x) =
√(x) and ​g(x) = x cubed plus 8​, simplify the expressions (f circle g )(2 )​, (f circle f )(25 )​, (g circle f )(x )​, and (f circle g )(x ).

User Cthulhu
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Answer:

Explanation:

Given are two functions f and g defined as


f(x) =√(x) \\g(x) = x^3+8

we have to find the composition of functions in all orders

1)
a)(fog)(x)=f{g(x)}=f(x^3+8) =√(x^3+8) \\\\(fog)(2) = =4,-4


b) (fof)(x) = f{f(x)}=f(√(x) {=\sqrt[4]{x} \\\\When x=25, ans= √(5)


c) (gof)(x) = g(√(x)) = (√(x))^3+3 = x^{(3)/(2) } +8\\\\d)(fog)(x)=f{g(x)}=f(x^3+8)

User Artem Kozlenkov
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