# Solving for H(g(f(x)))

• Feb 15th 2010, 07:19 AM
Sarcasticus
Solving for H(g(f(x)))
Hi, i've been posed a maths tutorial on functions and i'm just looking for someone to check my answer. I would get a classmate or lecturer to do it, but it's reading week and no-one is around.

So, With that in mind.

Given f(x)= 4x + 6 , g(x)= 2xSquared -3x + 5, and h(x)= 6x, find h(g(f(x)))

f(x)=4x-6
g(f(x))= 2(4x-6)squared -3(4x-6) + 5
-> 2(16x -36) -3(4x-6) + 5
-> (32x - 72) (12x-18) + 5
-> (44x - 90 + 5)
h(g(f(x))) = 6(44x - 90 + 5)
->(264x 540 + 30)

h(g(f(x)))= 264x -540 + 30

correct?

Did i mess up along the way or does this look right?
Any pointers you can give me would be good, as well as a way to display the character for squared, cubed etc. thanks in advance. Also apologies if i got this in the wrong forum.
• Feb 15th 2010, 07:41 AM
NeilT
You're method looks good to me but you've been a little careless when multiplying out the brackets, note that:

\$\displaystyle 2(4x + 6)^2
=2(4x + 6)(4x + 6)
=2(16x^2 + 48x + 36)
=32x^2 + 96x + 72\$

Hope this helps
• Feb 15th 2010, 07:41 AM
Sarcasticus
ok, thank you, ill go back and redo.
• Feb 15th 2010, 07:48 AM
Sarcasticus
Quote:

Originally Posted by NeilT

\$\displaystyle 2(4x + 6)^2
=2(4x + 6)(4x + 6)
=2(16x^2 + 48x + 36)
=32x^2 + 96x + 72\$

could you go into a little more detail explaining the steps done?

such as how you got the \$\displaystyle 16x^2\$? thanks.
• Feb 15th 2010, 07:55 AM
NeilT
Quote:

Originally Posted by Sarcasticus
could you go into a little more detail explaining the steps done?

such as how you got the \$\displaystyle 16x^2\$? thanks.

Ok so, for simplicity lets ignore the 2 at the start as we can just double at the end to get our answer. When we multiply two brackets together we use the "distributive law" for multiplcation whch basically says take each element of the frst bracket and multiply it by every term in the next bracket eg:

\$\displaystyle (a + b)(c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd\$

or as in this case

\$\displaystyle (4x + 6)(4x + 6) = 4x(4x + 6) + 6(4x + 6) = 16x^2 + 24x + 24x + 36 = 16x^2 + 48x +36\$

Hope that clears it up for you
• Feb 15th 2010, 08:06 AM
Sarcasticus
Thanks. I think i get the whole \$\displaystyle 4x * 4x\$ becoming \$\displaystyle 16x^2\$. \$\displaystyle 4 x 4 = 16, and X * X = x^2\$, most teachers dont explain that particular bit has 2 mini parts.

Thanks again, you've saved my bacon.