Solve the function. Let g(x) = −7+2/x Solve for x if g(x) = -3.

Question

asked Jul 27, 2023 118k views

1 Answer

Lennyy · Answer 1 · 2023-08-01T12:31:09+0000

Hello !

Answer:

$\boxed{\sf x=(1)/(2) }$

Explanation:

Our objective is to determine the value of x that fulfills the given equation :

$\sf g(x)=-3$

First of all, it is important to note that the function is not defined at 0 because dividing by 0 is not possible.

Let's replace f(x) with its expression in the equation :

$\sf -7+(2)/(x) =-3$

Mutliply both sides by x :

$\sf x(-7+(2)/(x) )=-3x$

Expand the left side :

$\sf -7x+2=-3x$

Now, let's add 3x to both sides and combine like terms :

$\sf -7x+2+3x=-3x+3x\\-4x+2=0$

Let's substract 2 from both sides :

$\sf -4x+2-2=-2\\-4x=-2$

Finally, let's divide both sides of the equality by -4 :

$\sf (-4x)/(-4) =(-2)/(-4)\\ \boxed{\sf x=(1)/(2) }$

Have a nice day ;)