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1) Using f(x) = 6x² and g(x) = 14x + 4 find:
(f °g)(x)
(g°f)(x)
2) Using f(x) = 8x and g(x) = 4x t 2 find:
(g°g) (x)
(f°f) (x)
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Show solution
1) Using f(x) = 6x² and g(x) = 14x + 4 find:
(f °g)(x)
(g°f)(x)
2) Using f(x) = 8x and g(x) = 4x t 2 find:
(g°g) (x)
(f°f) (x)
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Answer:
1) f(g(x)) = 6(14x + 4)^2 = 6(196x^2 + 112x + 16)
g(f(x)) = 14(8x^2) + 4 = 112x^2 + 4
2) g(g(x)) = 4(4x^2) = 16x^2
f(f(x)) = 8(8x^2) = 64x^2
Step-by-step explanation:
1) We start with the function f(x) = 6x². To find f(g(x)), we plug in the g(x) values into f(x). So, we have f(g(x)) = 6(14x + 4)^2. This simplifies to 6(196x^2 + 112x + 16).
2) To find g(f(x)), we plug in the f(x) values into g(x). So, we have g(f(x)) = 14(8x^2) + 4. This simplifies to 112x^2 + 4.
3) To find (g°g)(x), we plug in the g(x) values into g(x) again. So, we have (g°g)(x) = 4(4x^2). This simplifies to 16x^2.
4) Finally, to find (f°f)(x), we plug in the f(x) values into f(x) again. So, we have (f°f)(x) = 8(8x^2). This simplifies to 64x^2.