## anonymous one year ago A graph of 2 functions is shown below. graph of function f of x equals negative 2 multiplied by x plus 3 and graph of function g of x equals x cubed plus 4 multiplied by x squared minus x minus 4 Which of the following is an approximate solution for f(x) = g(x)? x = 1 x = −1 x = −4 x = 2

1. anonymous

@Vocaloid

2. anonymous

@ospreytriple

3. anonymous

@Michele_Laino

4. anonymous

@LiveLaughDie

5. Plasmataco

Set the 2 equations to equal each other

6. Michele_Laino

the equations of your functions, are: $\Large \begin{gathered} f\left( x \right) = - 2x + 3 \hfill \\ g\left( x \right) = {x^3} + 4{x^2} - 4 \hfill \\ \end{gathered}$ now, you have to establish, what vauel of x, among that you have listed above, is the one such that g(x)=f(x)

7. Michele_Laino

value*

8. Plasmataco

U get 2x+3=X powered 3+4x powered 2-x-4

9. anonymous

okay :]

10. Plasmataco

Simplify it so that 0 is on one side

11. Michele_Laino

for example, let's consider x=-1, then we have: $\Large \begin{gathered} f\left( { - 1} \right) = - 2 \cdot \left( { - 1} \right) + 3 = 5 \hfill \\ g\left( { - 1} \right) = {\left( { - 1} \right)^3} + 4{\left( { - 1} \right)^2} - 4 = - 1 + 4 - 4 = - 1 \hfill \\ \end{gathered}$ so our value for x, can not be x=-1

12. Plasmataco

Now u get X powered 3+4x powered 2+x-7

13. Plasmataco

Which is all. Equal to 0

14. anonymous

okay :]

15. Plasmataco

Now, factor is to some thing like (x+a)(x+b)(x+c)

16. Michele_Laino

plese, try with x=1, namely replace x with 1, into both functions f(x), and g(x), what do you get?

17. anonymous

ok give me 1 min ;]

18. Michele_Laino

19. anonymous

$f(−4)=−2⋅(−4)+3=5g(−4)=(−4)^3+4(−4)^2−4=-4+4−4=-4?$

20. Plasmataco

I'll let u do it @Michele_Laino s way but with this, u get an approximation of 1

21. Michele_Laino

we have: $\Large \begin{gathered} f\left( { - 4} \right) = - 2\left( { - 4} \right) + 3 = 11 \hfill \\ g\left( { - 4} \right) = {\left( { - 4} \right)^3} + 4{\left( { - 4} \right)^2} - 4 = - 64 + 64 - 4 = - 4 \hfill \\ \end{gathered}$

22. anonymous

Oh

23. Michele_Laino

please compute these quantities: $\Large \begin{gathered} f\left( 1 \right) = ... \hfill \\ g\left( 1 \right) = ... \hfill \\ \end{gathered}$

24. anonymous

So its 1?

25. Michele_Laino

we have: $\Large \begin{gathered} f\left( 1 \right) = - 2 \cdot 1 + 3 = - 2 + 3 = 1 \hfill \\ g\left( 1 \right) = {1^3} + 4 \cdot {1^2} - 4 = 1 + 4 - 4 = 1 \hfill \\ \end{gathered}$

26. Michele_Laino

so, it is x=1

27. anonymous

Thank you!

28. Michele_Laino

:)

29. anonymous

Can you check one for me?

30. Michele_Laino

ok!

31. anonymous

Wait nvm! I got it !Thank you!

32. Michele_Laino

ok! :)