1. Composite functions

hello everyone! im new to this forum, found it by google because i couldnt find an answer anywhere else, i am trying to study for a college placement test and i am having some trouble trying to remember math i learned 3 years ago, here is the link to the math sample questions:

Code:
http://www.nvcc.edu/woodbridge/TCenter/mathsample.htm
i am stuck on number 39, second part. If g is a function such that g(x) = ax^2 –3 and g(3) = 3, find g(6). (answer: 21)

i need to know the process of how to do it, many thanks everyone!!

2. Hi! micro31337
g(x)=ax^2-3
g(3)=3 therfor
a(3)^2-3=3
9a=6
a=2/3
therfor g(x)=(2/3 )x^2-3
so g(6)=(2/3) (6)^2-3 = 24-3 =21

3. Originally Posted by micro31337
hello everyone! im new to this forum, found it by google because i couldnt find an answer anywhere else, i am trying to study for a college placement test and i am having some trouble trying to remember math i learned 3 years ago, here is the link to the math sample questions:

Code:
http://www.nvcc.edu/woodbridge/TCenter/mathsample.htm
i am stuck on number 39, second part. If g is a function such that g(x) = ax^2 –3 and g(3) = 3, find g(6). (answer: 21)

i need to know the process of how to do it, many thanks everyone!!
here is how function notations work. whatever shows up in the brackets, we put it in place of the x in the formula (as long as it is in the domain of the function.

$g(x) = ax^2 - 3$

$\Rightarrow g({\color{red}3}) = a({\color{red}3})^2 - 3 = 9a - 3$

now, we are told that g(3) = 3, thus:

$9a - 3 = 3$

$\Rightarrow 9a = 6$

$\Rightarrow a = \frac 23$

therefore, $g(x) = \frac 23x^2 - 3$

now, can you tell me what $g(6)$ is?

4. wow omg thank you! i understand now! i knew i had to something like that but i didnt understand it because of the g(3) and g(6), there were 2 so i didnt know which one to use or why there are 2,and then there was the "a" . thank you so much, you guys reply fast i love this place!