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Composition Of Functions
Composing functions involves taking two functions, f(x) and g(x), and substituting the output of g(x) wherever x appears in f(x). For the functions f(x) = 3x^2 + 4 and g(x) = 6x - 8, the composition f(g(x)) is found by substituting g(x) = 6x - 8 for x in f(x), giving f(g(x)) = 3(6x - 8)^2 + 4, which simplifies to 108x^2 - 288x + 22.
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Composition Of Functions
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- 3. Basic composing usestwo functions. We will call them f(x) and g(x).
- 4. Composition of Functions f(x)= 3x2 + 4 and g(x) = 6x - 8
- 5. Composition of Functions Ifthe composition is f(g(x)), (f of g of x), simply insert the g(x) function wherever an x appears in the f(x) function.
- 6. Composition of Functions So,f(g(x)) = f(6x - 8) = 3(6x - 8)2 + 4
- 7. Composition of Functions Thensimplify the equation.
- 8. Composition of Functions =3(6x - 8)2 + 4 = 3(6x - 8)(6x - 8) + 4 = 3(36x2 - 48x - 48x + 6) + 4 = 3(36x2 - 96x + 6) + 4 = 108x2 - 288x + 18 + 4 = 108x2 - 288x + 22