## Adi3 one year ago Will Medal!!! Please help Suppose f(x) = 3x+1 and g(x) = x^2 +2x. Find x such that f(g(x)) = 10.

@ganeshie8

2. anonymous

Use Wolfram alpha for this

wolfram alpha is not correct

4. DanJS

replace each x value in f(x) with the entire function g(x)

5. DanJS

f(x) = 3x+1 f(g(x)) = 3*g(x) + 1

What do you mean by that?

7. DanJS

g(x) = x^2+2x f(g(x)) = 3*g(x) + 1 = 3 * (x^2 + 2x) + 1

8. DanJS

see that

yeah i get it

10. DanJS

then they tell you that equals to a value and find x

it equals 3x^2 + 6x + 1 right

12. DanJS

10 = 3x^2 + 6x + 1

13. DanJS

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

15. DanJS

it is a quadratic, to get the solution, you put it in standard form first.. ax^2+bx+c=0

16. DanJS

3x^2 + 6x - 9 = 0 3*( x^2 + 2x - 3) = 0

then what to do next

18. DanJS

so, x^2 + 2x -3 = 0 you can always just apply the quadratic formula, but this one looks to factor easy

19. DanJS

(x - 1)*(x+3) = 0

wait from where did x-1 come from

21. DanJS

so, that is true if.. x - 1 = 0 OR x + 3 = 0

22. DanJS

x = 1 or x=-3

23. DanJS

ohh thanks

25. DanJS

distribute the thing and check , it goes back to the original

26. DanJS

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

29. DanJS

divide both sides with a 3

30. DanJS

0/3 = 0

31. DanJS

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

33. DanJS

$x = \frac{ -b \pm \sqrt{b^2 - 4*a*c} }{ 2a }$

34. DanJS

k, welcome