Question

A graph of two functions is shown below:

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

Which of the following is a solution for f(x) = g(x)?

x = −2
x = 1
x = 0
x = −1

Answer 1

Answer: x = 1

Explanation:

The solution is simply the point where the two lines intersect on the graph. In this problem, the two lines cross each other at 1, so that would be the solution.

Answer 2

The solution to the given functions f(x) and g(x) is 1

Therefore f(x)=g(x)=0 when x=1

Explanation:

Given that the functions f(x) and g(x) defined as below

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

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

To verify that the solution satisfies f(x)=g(x) :

Put x=1 in f(x) and g(x) we get

`f(x)=(-11(1))/(3)+(11)/(3)`

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

`=0`

Therefore f(x)=0 when x=1

put x=1
`g(1)=1^3+2(1)^2-1-2`

`=1+2-1-2`

`=0`

Therefore g(x)=0 when x=1

Therefore f(x)=g(x)=0 when x=1

Therefore the solution to the given functions f(x) and g(x) is 1.