If f(x)=3x and g(x)=2x-6 find (g o g)(x)

Question

anonymous · Answer

g(g(x))  ??

Put x = 2x - 6 in g(x)..

unklerhaukus · Answer

$$(g\circ g)(x)=g(g(x))=g(2x-6)=dots$$

anonymous · Answer

for the "dots' replace the "$x$" in $2x-6$ by $2x-6$

anonymous · Answer

Replace the x with what ?

anonymous · Answer

or if you prefer, replace the $\diamondsuit$ in $2\diamondsuit -6$ by $2x-6$

anonymous · Answer

let me write it out for you 
$$g(g(x))=g(2x-6)=2(2x-6)-6$$ then some algebra to clean it up

anonymous · Answer

celeste wants to have her hair cut and permedand also go to lunch .she knows she will need $59 . the perm cost twice as much as her hair cut and she needs $5 for lunch . how much does the perm cost ?

anonymous · Answer

don't let all the "$x$'s confuse you
the function is not "two ex minus six" the function says "take the input, multiply it by 2, then subtract 6"

anonymous · Answer

so if i have $g(5)$ it is $2\times 5-6$ and if i have $g(\heartsuit)$ it is $2(\heartsuit)-6$ and 
$$g(\heartsuit +\clubsuit)=2(\heartsuit +\clubsuit)-6$$
and so 
$$g(2x-6)=2(2x-6)-6$$

anonymous · Answer

no my problem is :celeste wants to have her hair cut and permedand also go to lunch .she knows she will need $59 . the perm cost twice as much as her hair cut and she needs $5 for lunch . how much does the perm cost ?

anonymous · Answer

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anonymous · Answer

Okay thank you. i figured it out. you were very helpful;. you deserve a medal !!!