We conclude that if we define:
f(x) = x^2
g(x) = 9x + 5
Then the composition (f ∘ g)(x) is equal to h(x).
How to find the two functions f(x) and g(x)?
Here we want to find two functions f(x) and g(x) such that their composition (remember that the composition of two functions means that we are evaluating the first function in the second function, this would mean that (f ∘ g)(x) = f(g(x))) is equal to the function h(x).
Where h(x) = (9x + 6)^2
Now, if you look at the function h(x), you can see that it is a linear equation squared.
Then we can define g(x) as that linear equation and f(x) as a quadratic function, such that we have:
f(x) = x^2
g(x) = 9x + 5
When we compose these two functions, we get:
(f°g)(x) = f( g(x)) = g(x)^2
Now we can replace "g(x)" by the actual function, then:
(f ∘ g)(x) = (9x + 5)^2
In this way, we conclude that if we define:
f(x) = x^2
g(x) = 9x + 5
Then the composition (f ∘ g)(x) is equal to h(x).
If you want to learn more about the composition of functions:
https://brainly.com/question/10687170
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