Question

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

Answer 1

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 ;)