Question

Based on the graph below, what is the total number of solutions to the equation f(x) = g(x)?

graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2

One
Two
Three
Four

Answer 1

the answer is One

Explanation:

A solution is where the two lines intersect on the graph, and as you can see, in the picture above, the two lines only intersect once

Answer 2

The total number of solutions is one

Explanation:

we have

`f(x)=-(11)/(3)x+ (11)/(3)`

`g(x)=x^(3)+2x^(2)-x-2`

To solve the system of equations equate f(x) and g(x)

`f(x)=g(x)`

The solution of the system of equations is the intersection points both graphs

Using a graphing tool

see the attached figure

The solution of x

`x=1`

There is only one point of intersection both graphs

therefore

The total number of solutions is one