Let f(x) = 3x + 2 and g(x) = 2x - 4. Find (f ° g)(x) and (g ° f)(x)
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Solve |
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(f og)(x) = f(g(x)) = f(2x - 4) |
Substitute g(x) into f(x) | |
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= 3(2x - 4) + 2 = 6x - 12 + 2 = 6x - 10 |
We have a new function 6x - 10 | |
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(g of)(x) = g(f(x)) = g(3x + 2) |
Substitute f(x) into g(x) | |
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= 2(3x + 2) - 4 = 6x + 4 - 4 = 6x |
We have a new function 6x | |
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Notice that 6x - 10 ¹ 6x (f og)(x) and (g o f)(x) may not be equal |
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