Question

Need help with 2 and 4 ASAP Inverses...

Answer 1

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.