MHB F(x) = x2-7 and g(x) = x- 3, find (f º g )(x) [2]

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To find (f º g)(x), substitute g(x) into f(x), resulting in (x - 3)² - 7. For (g º f)(x), substitute f(x) into g(x), yielding x² - 7 - 3. The discussion also touches on finding the inverse functions f⁻¹(x) and g⁻¹(x), but the focus remains on the composition of the functions. The user expresses confusion about the notation and seeks clarification on how to proceed with the calculations. Understanding function composition is crucial for solving these problems effectively.
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Let f(x) = x2-7 and g(x) = x- 3
Find:
i. (f º g )(x) [2]
ii. (g º f) (x) [2]
iii. f-1 (x) = g-1(x)
 
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trevor said:
Let f(x) = x2-7 and g(x) = x- 3
Find:
i. (f º g )(x) [2]
ii. (g º f) (x) [2]
iii. f-1 (x) = g-1(x)

Hi trevor. What have you tried so far? :)
 
Joppy said:
Hi trevor. What have you tried so far? :)

I am clueless
 
(f o g)(x) means f(g(x)). That means, you replace the value in f(x) with g(x), thus your x2 - 7 will become (g(x))2 - 7. Can you continue from here?
 

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