2.
h(x) = 1/(x - 1)
Replace h(x) with y.
y = 1/(x - 1)
Swap x and y.
x = 1/(y - 1)
Solve for y.
Multiply both sides by (y - 1)
x(y - 1) = 1
Distributive property.
xy - x = 1
Add x to both sides.
xy = 1 + x
Divide both sides by x.
y = 1/x + 1
Replace y with h^-1(x)
H^-1(x) = 1/x + 1 is the inverse function for question 2.
4.
h(x) = 4/(x + 2)
Replace h(x) with y.
y = 4/(x + 2)
Swap y and x.
x = 4/(y + 2)
Solve for y.
Multiply both sides by y + 2.
x(y + 2) = 4
Distributive property.
xy + 2x = 4
Subtract both sides by 2x.
xy = 4 - 2x
Divide both sides by x.
y = 4/x - 2
Replace y with h^-1(x)
H^-1(x) = 4/x - 2 is the inverse function for question 4.