Math help for medal!!

Question

dontknowdontcare · Answer

If h(x)= x^2-3x and g(x)=2x+4 find (h of g)(x)

mathmale · Answer

First of all:  Have you done other problems of this kind before?
If so, what have you learned from them that you could apply here?

satellite73 · Answer

step one in computing $$h\circ g(x)$$ is to get rid of the circle notation and write is as $$h(g(x))$$

satellite73 · Answer

step two is to replace the general $g(x)$ by the specific one you have so step two is $$h(2x+4)$$

satellite73 · Answer

step 3
since $$h(\spadesuit)=\spadesuit^3-3\spadesuit$$
then $$h(2x+4)=(2x+4)^2-3(2x+4)$$

satellite73 · Answer

step 4 is to do the algebra
multiply out, combine like terms

dontknowdontcare · Answer

so far I have 4x^2+8x+8x+16-6x+12 and then I subtracted the 6x from the second 8x and added the 12 to the 16 leaving me with; 4x^2+8x+2x+28 then I grouped and now have 4x(x+2) 2(x+14) which I know isnt correct because they have to be the same...where did I mess up?

satellite73 · Answer

you didn't distribute the minus sign

satellite73 · Answer

$$ 4x^2+8x+8x+16-6x+12 $$should be $$ 4x^2+8x+8x+16-6x-12 $$

satellite73 · Answer

in other words $$-3(2x+4)=-3x-12$$
it is a common mistake (how i found it right away)

dontknowdontcare · Answer

thanks!

dontknowdontcare · Answer

so should the equation leave off with -3x-12, or should I simplify it by grouping?

mathmale · Answer

Any valid simplification is worth doing.