Will Medal!!! Please help Suppose f(x) = 3x+1 and g(x) = x^2 +2x. Find x such that f(g(x)) = 10.

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Will Medal!!! Please help Suppose f(x) = 3x+1 and g(x) = x^2 +2x. Find x such that f(g(x)) = 10.

Mathematics
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Use Wolfram alpha for this
wolfram alpha is not correct

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replace each x value in f(x) with the entire function g(x)
f(x) = 3x+1 f(g(x)) = 3*g(x) + 1
What do you mean by that?
g(x) = x^2+2x f(g(x)) = 3*g(x) + 1 = 3 * (x^2 + 2x) + 1
see that
yeah i get it
then they tell you that equals to a value and find x
it equals 3x^2 + 6x + 1 right
10 = 3x^2 + 6x + 1
yeah the f(g(x)) does, then they tell you that is equal to 10
then how do you solve it after that, that s the part which is the most confusing for me
it is a quadratic, to get the solution, you put it in standard form first.. ax^2+bx+c=0
3x^2 + 6x - 9 = 0 3*( x^2 + 2x - 3) = 0
then what to do next
so, x^2 + 2x -3 = 0 you can always just apply the quadratic formula, but this one looks to factor easy
(x - 1)*(x+3) = 0
wait from where did x-1 come from
so, that is true if.. x - 1 = 0 OR x + 3 = 0
x = 1 or x=-3
factoring a quadratic
ohh thanks
distribute the thing and check , it goes back to the original
or simply just plug in the coefficients to the quadratic equation and hit a button to solve for you
i did not get the part after this 3x^2 + 6x - 9 = 0 3*( x^2 + 2x - 3) = 0
what did you do after this
divide both sides with a 3
0/3 = 0
Once you get down to standard form ax^2 + bx + c = 0 solving that expression for x will give you the quadratic formula
yeah i get it, thanxs
\[x = \frac{ -b \pm \sqrt{b^2 - 4*a*c} }{ 2a }\]
k, welcome
thnxs

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