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If f(x)=x^2-2 and g(x)=x-3, what is (f*g)(x)?

If f(x)=x^2-2 and g(x)=x-3, what is (f*g)(x)?-example-1

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This is a composite that could also be written in the form f(g(x)). Take the function defined as g(x) and stick it in in place of the x in f(x). Like this:
f(g(x))=(x-3) ^(2) -2. And that's it.
User Florakel
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4 votes
For this case we have the following functions:

f (x) = x ^ 2 - 2 g (x) = x - 3
We must make the following composition of functions:

(fog) (x)
This composition of functions means that we must replace the function g (x) in the function f (x) in the following way:

f (g (x))
We have then:

f (g (x)) = (x - 3) ^ 2 - 2
Rewriting we have:

f (g (x)) = x ^ 2 - 6x + 9 - 2 f (g (x)) = x ^ 2 - 6x + 7
Answer:

f (g (x)) = x ^ 2 - 6x + 7
option 2
User Dzejms
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