For the following functions f&g, f(x)=9x^2-4x+8 & g(x)=2√x determine

(a) f(g(x)) (b) f(f(x))

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Composite Function

A) f(g(x))=9(2√x)^2-4(2√x)+8

B) f(f(x))=9(9x^2-4x+8)^2-4(9x^2-4x+8)+8

Given:

f(x) = 9x2 - 4x + 8 and

g(x) = 2√x

To solve :

A] f(g(x))

B] f(f(x))

Solution :

A] f(g(x))

= f(2√x)

= 9(2√x)2 - 4(2√x) + 8

= **36x - 8√x + 8**

B] f(f(x))

= f(9x2 - 4x + 8)

= 9(9x2 - 4x + 8)2 - 4(9x2 - 4x + 8) + 8

= 729x^4 - 648x^3 + 1440x^2 - 576x + 576 - 36x2 + 16x -32 + 8

= **729x^4 - 648x^3 + 1404x^2 - 560x + 552**

Hope this helps!

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