someone explain this function problem please?

[spoog74]

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if G(f(x))= x^2-3 and g(x) = x-3 then find F(3).


The answer given is 9

can someone explain HOW thats the answer?

Thanks !!

 

[Internationall]

Since g(x) = x-3, then g(f(x))=f(x)-3.
<Since x could be anything, here we let x=f(x)>

Also, we know that g(f(x))= x^2-3, as it is given.
Therefore f(x)-3=x^2-3.
Solve for f(x), you get f(x)=x^2.
Plug in x=3, then 3^2=9.

Looks bad but it's not. Trust me!🙂