# If f(x)=3x^2-4 and g(x)=2x-1, what is (f * g)(x)?

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### 2 Answers

I suppose the * means composition of function.

Similarly (f *g)(x) = f(g(x)).

If that is the case, we replace the x on f(x) by 2x - 1.

`(f * g)(x) = f(g(x)) = 3(2x - 1)^2 - 4`

Use foil method on (2x - 1)^2 = (2x - 1)(2x - 1).

`(f * g)(x) = 3(4x^2 - 4x + 1) - 4`

Use Ditributive Property.

`(f * g)(x) = 12x^2 - 12x + 3 - 4`

Hence, final answer will be:

**(f * g)(x) = 12x^2 - 12x - 1 **

`f(x)=3x^2-4` `g(x)= 2x-1`

`f[g(x)]= 3(2x-1)^2-4=3(4x^2-4x+1)-4=`

`=12x^2-12x+3-4=12x^2-12x-1`

Note that product isn't abelian indeed:

`g[f(x)]=2(3x^2-4)-1=6x^2-8-1=3(2x^2-3)`

so:

`f[g(x)] != g[f(x)]`