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Hello Pawan --

I'm having some difficulty understanding what is meant transformation. I've been given the equations :

f(x)= x^3-2x^2+x and g(x)= 3f(x+1)-2

Now, I've received your explanation of how f(x+1) = x^3 + 3x^2 + 3x +1. This is fine, BUT what I don't understand is how to LIST the transformation of f(x) to OBTAIN g(x).

Can you help me with this?

Thanks...Angelo

Angelo,

What I understand is that you want to write/list g(x) in the terms of f(x) and not f(x+1).

Now as we have got f(x+1) = x^3 + 3x^2 + 3x +1, we will rewrite it in terms of f(x).

We know that f(x) = x^3-2x^2+x. Hence we will rearrange f(x+1) to include terms x^3-2x^2+x in its equation as given below:

f(x+1) = x^3 + 3x^2 + 3x +1

= x^3 + 5x^2-2x^2 + x+2x + 1

As you can see here, the equation remains the same but we have broken it down to include terms of f(x). We can rewrite it as,

f(x+1) = x^3-2x^2+x +5x^2+2x+1

= f(x) + 5x^2+2x+1

Thus we get,

f(x+1) = f(x) + 5x^2+2x+1 ...........................(1)

Now,

g(x)=3f(x+1)-2

We will write f(x+1) in terms of f(x) as derived in equation (1) above.

g(x) = 3[f(x) + 5x^2+2x+1] - 2

= 3f(x) + 15x^2 + 6x +3 -2

= 3f(x) + 15x^2 + 6x + 1 ...................... (2)

I hope that this is what you are looking for. Please let me know if you need additional information.

Regards,

Pawan

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