Question

Find the composition of f(g(x)), when
f(x)=7x^2-2x+9 and
g(x)=x-4
Simplify

Answer 1

I have a pretty clear idea of how to go about doing this, so I'll just show all of my process. I'll also point out the one small detail that I had a bit of doubt on.

Answer 2

\(7(x-4)^{2}-2(x-4)+9\)

\(7(x-4)(x-4)-2x+8+9\)

\((7x-28)(x-4)-2x+17\)

\(7x^{2}-28x-28x+112-2x+17\)

\(7x^{2}-58x+129\)
^^
I believe this is correct...but I forget the rules on difference of squares.
does (x-2)^2 turn into (x-2)(x-2) or (x-2)(x+2) ??

Also, do I need to factor the final answer?

Answer 3

try and see if it can be done,then its good

Answer 4

see it what can be done?

Answer 5

i don't think it can be factored

Answer 6

x^2 means x times x

anything squared is that number multiplied by itself

so (x-2)^2 means (x-2) times (x-2)

Answer 7

\[\Large 7x^{2}-58x+129\] is the correct final answer

Answer 8

Oh. You're referring to my question on whether it could be factor or not.

oh and @jim_thompson5910 , so in the problem, if you look at my work, my assumption was indeed that (x-2)^2 was (x-2)(x-2). Thank you! I thought I remembered some funky rule from early high school about difference of squares or something like that. So I was correct all along. Wow I overthought this. Thank again!

Answer 9

you're thinking of a^2 - b^2 = (a-b)(a+b)

Answer 10

its perfectly all right

Answer 11

u can solve it by the formula

Answer 12

Oh okay. These rules are so easy to get confused, especially when trying to recall from memory

Answer 13

this formula is known as the SRIDHAR ACHARYA formula

Answer 14

don't worry by this formula it will get easy

Answer 15

put 7x^-58x+129 in this formula

Answer 16

Don't you mean the quadratic formula? And yes, I know that you can use the quadratic formula to factor. Problem is, I see now that when I use the quadratic formula, the roots are imaginary. Therefore, This cannot be factored any further. Jim's answer is the final answer

Answer 17

yeah

Answer 18

@madhu.mukherjee.946 thanks for trying to help, but I fully understand now. I've used the quadratic formula before, and I understand what it does \(\ddot\smile\)

Answer 19

okay.your welcome

Answer 20

You can use the discriminant formula as a shorter way to see if you can factor or not

if D = b^2 - 4ac is a perfect square and a positive number, then you can factor

Answer 21

Woah, that's a helpful tip. *cough* I have a program in my calculator that solves all quadratics for me, so that's how I knew that the roots would be imaginary. But when in a pinch, when without a calculator, this is an extremely convenient tip. Thanks for bringing that back into my memory

Answer 22

definitely a handy thing to have

Answer 23

you're welcome