Inverse of g(x)= 6/(4-x)
g(x)= 6/(4-x)
y = 6/(4-x)
step 1, interchange the x and y variables:
x = 6/(4-y)
step 2. solve this new equation for y
4x - xy = 6
4x - 6 = xy
y = (4x - 6)/x
g^-1 (x) = (4x-6)/x
check : with a couple of values of x
g(1) = 6/(4-1) = 2
g^-1 (2) = (8-6)/2 = 1, ok
g(-2) = 6/(4+2) = 1
g^-1 (1) = (4-6)/1 = -2, ok
This does not "probe" that my answer is correct, but shows
that it is highly likely that it is correct.
g = 6/(4-x)
4-x = 6/g
x = 4 - 6/g
so g-1(x) = 4 - 6/x
check
g-1(g(x)) = 4 - 6/g(x)
= 4 - 6/(6/(4-x))
= 4 - (4-x)
= x