# Thread: Find Simplified Expression for g(x)

1. ## Find Simplified Expression for g(x)

If f(x)=2x^2-3x+1, find the simplified expression for g(x) in
g(x)= f(2x).

2. Replace every $\displaystyle x$ in $\displaystyle f(x)$ with $\displaystyle 2x$.

Then simplify.

3. Let x = 2x for f(x)

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

f(2x) = 2(4x^2) - 6x + 1

f(2x) = 8x^2 - 6x + 1

Correct?

4. Originally Posted by fdrhs1984
Let x = 2x for f(x)

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

f(2x) = 2(4x^2) - 6x + 1

f(2x) = 8x^2 - 6x + 1

Correct?
Yes, good job.

5. Great! Thanks a lot.

6. Originally Posted by fdrhs1984
Let x = 2x for f(x)

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

f(2x) = 2(4x^2) - 6x + 1

f(2x) = 8x^2 - 6x + 1

Correct?
Yes it is.

You could also simplify further by factorising.

$\displaystyle f(2x) = 8x^2 - 6x + 1$

$\displaystyle = 8x^2 - 4x - 2x + 1$

$\displaystyle = 4x(2x - 1) - 1(2x - 1)$

$\displaystyle = (2x - 1)(4x - 1)$.

7. Is this the Grouping Method for factoring?

8. Originally Posted by fdrhs1984
Is this the Grouping Method for factoring?
It most certainly is.

Multiply your $\displaystyle a$ and $\displaystyle c$ values. In this case you get $\displaystyle 8$.

So you need to think of two numbers that multiply to give $\displaystyle 8$ and add to give $\displaystyle -6$ (the $\displaystyle b$ value). In this case they are $\displaystyle -4$ and $\displaystyle -2$, which is what you break the middle term into.