Question

The graphs of f(x) and g(x) are shown below:

Graph of function f of x equals x squared minus x minus 12. Graph of function g of x equals negative 1.8 times x minus 0.6

What are the solutions to the equation f(x) = g(x)?

A.)x = −3, 4
B.)x = −3.8, −0.4
C.)x = −3.8, 3
D.)x = 6.5, −6

Answer 1

C

Explanation:

I took the test

Answer 2

Option: C is the correct answer.

C.) x = −3.8, 3

Explanation:

The function f(x) is given by:

`f(x)=x^2-x-12`

and the function g(x) is given by:

`g(x)=-1.8x-0.6`

Now, we are asked to find the solution of the equation:

`f(x)=g(x)`

i.e. we have to find the value of x such that both the functions are equal i.e.

`x^2-x-12=-1.8x-0.6\\\\i.e.\\\\x^2-x+1.8x-12+0.6=0\\\\i.e.\\\\x^2+0.8x-11.4=0\\\\i.e.\\\\10x^2+8x-114=0\\\\i.e.\\\\5x^2+4x-57=0`

Now, on solving the equation using the quadratic formula i.e. the solution of the equation:

`ax^2+bx+c=0`

is given by:

`x=(-b\pm √(b^2-4ac))/(2a)`

Here we have:

`a=5,\ b=4\ and\ c=-57`

Hence, the solution is given by:

`x=(-4\pm √(4^2-4* 5* (-57)))/(2* 5)\\\\i.e.\\\\x=(-4\pm √(16+1140))/(10)\\\\i.e.\\\\x=-3.8\ and\ x=3`