Find the inverse function of  g(x) = -2/(x+1)

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

let y= -2/(x+1)

Now we will multiply by (x+1) both sides:

==> y(x+1) * -2(x+1)/(x+1)

Now eliminate similar:

==> y(x+1) = -2

Now we will diustribute y:

==> yx + y = -2

Now we will subtract y from both sides:

==> yx = -2 - y

Now divide by y:

==> x = (-2-y)/y

==> x= (-2/y) - y/y

==> x= -2/y -1

Now we will subsitute with x and y:

==> y= -2/x - 1

Then the inverse function is:

f^-1 (x) = -2/x - 1

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The inverse function of g(x) could be found in this way.

We'll note g(x) = y

y = -2/(x+1)

Now, we'll try to find x with respect to y. For this reason, we'll cross multiply:

y(x+1) = -2

We'll remove the brackets and we'll get:

yx + y = -2

We'll isolate x to the left side and we'll get:

yx = -2 - y

We'll divide by y:

x = -(2+y)/y

So, the inverse function is:

f^-1(x) = -(2+x)/x

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