Question

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

Answer 1

@Vocaloid

Answer 2

@ospreytriple

Answer 3

@Michele_Laino

Answer 4

@LiveLaughDie

Answer 5

Set the 2 equations to equal each other

Answer 6

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)

Answer 7

value*

Answer 8

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

Answer 9

okay :]

Answer 10

Simplify it so that 0 is on one side

Answer 11

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

Answer 12

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

Answer 13

Which is all. Equal to 0

Answer 14

okay :]

Answer 15

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

Answer 16

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

Answer 17

ok give me 1 min ;]

Answer 18

please*

Answer 19

\[f(−4)=−2⋅(−4)+3=5g(−4)=(−4)^3+4(−4)^2−4=-4+4−4=-4?\]

Answer 20

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

Answer 21

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

Answer 22

Oh

Answer 23

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

Answer 24

So its 1?

Answer 25

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

Answer 26

so, it is x=1

Answer 27

Thank you!

Answer 28

:)

Answer 29

Can you check one for me?

Answer 30

ok!

Answer 31

Wait nvm! I got it !Thank you!

Answer 32

ok! :)