What is the inverse function f(x)=(x+2)/(x+1)?

Question

What is the inverse function f(x)=(x+2)/(x+1)?

Answer 1

y = (x + 2)/(x+1)

Switch the x and y's around

x = (y + 2)/(y + 1)

Solve for y, first multiply the denominator over to left side

x(y+1) = y + 2

xy + x = y + 2  Now get the y terms on same side = non-y terms

xy - y = 2 - x  Factor out the y

y(x - 1) = 2 - x

y = (2 - x)/(x - 1)

Answer 2

y = (x+2)/(x+1)

x = (y+2)/(y+1)

xy + x = y + 2

y(x - 1) = 2 - x

y = (2 - x) / (x - 1)

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