Let f(x) = 2x2 + 3 and g(x) = x - 3. Find (f o g)(x) and (g o f)(x)
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Solve |
Step |
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(f og)(x) = f(g(x)) = f(x - 3) |
Substitute g(x) into f(x) | |
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= 2(x - 3)2 + 3 |
Don't forget the "+ 3" | |
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= 2(x2 - 6x + 9) + 3 |
(x - 3)2 = (x - 3)(x - 3) = x2 - 3x - 3x + 9 = x2 - 6x + 9 | |
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= 2x2 - 12x + 18 + 3 |
Simplify | |
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= 2x2 - 12x + 21 |
We have a new function: 2x2 - 12x + 21 | |
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(g of)(x) = g(f(x)) = g( 2x2 + 3) |
Substitute f(x) into g(x) | |
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= 2x2 + 3 - 3 |
Don't forget the "- 3" | |
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= 2x2 |
We have a new function: 2x2 - 3 | |
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Notice that 2x2 -
12x
+
21 ¹ 2x2
(f o g)(x) and
(g o f)(x)
may not be equal |
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