Math Help - 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 $x$ in $f(x)$ with $2x$.

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.

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

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

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

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

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 $a$ and $c$ values. In this case you get $8$.

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