Question

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

Answer 1

Answer:

Option: C is the correct answer.

            C.)   x = −3.8, 3

Step-by-step 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:

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here we have:

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

Hence, the solution is given by:

$x=\dfrac{-4\pm \sqrt{4^2-4\times 5\times (-57)}}{2\times 5}\\\\i.e.\\\\x=\dfrac{-4\pm \sqrt{16+1140}}{10}\\\\i.e.\\\\x=-3.8\ and\ x=3$