F(x)

[casper22]

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I came across this question in MATH Destroyer 2010 Test 2.

If G(F(x)) = x^2 -3 and G(x) = x-3, find F(3).

The solutions uses some comparison method, to determine F(x) = x^2 which I dont understand. How is this compared?

Thanks.

 

[ZFT]

1) given g(x) = x-3

2) then ask g(?) = x^2-3

3) deduce that g(x^2) = x^2-3

4) so f(x) = x^2

 

[casper22]

1) given g(x) = x-3

2) then ask g(?) = x^2-3

3) deduce that g(x^2) = x^2-3

4) so f(x) = x^2

Thanks man..that was so dumb of me..