Write the equation for the inverse of
Y= 4 Arccot (3x/4 - 2/3)

f(y) = (Cot(y) + 2/3)*(4/3)

Step-by-step explanation:

We have the function:

y = Arccot( 3*x/4 - 2/3)

And we want to find the inverse, then we must isolate x in the right side.

Applying cot( ) to both sides, we get

Cot( y) = Cot(Arccot( 3*x/4 - 2/3)) = 3*x/4 - 2/3

Cot(y) = 3*x/4 - 2/3

Cot(y) + 2/3 = 3*x/4

(Cot(y) + 2/3)*(4/3) = x

Then the inverse function is:

f(y) = (Cot(y) + 2/3)*(4/3)