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

Question

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

Answer 1

ƒ(x) = 1 / (x + 2)

Replace x with y and ƒ(x) with x:

x = 1 / (y + 2)

Solve for y. First, multiply by the denominator:

x·(y + 2) = 1

Divide by x:

(y + 2) = 1/x

Subtract 2:

y = 1/x - 2

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Alternatively, you can just get the recriprocals of both sides:

x = 1 / (y + 2)

1/x = (y + 2)/1

1/x - 2 = y

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Answer:

ƒ⁻¹ (x) = 1/x - 2

Answer 2

well, you simply reverse the equation.

so x+2, then inverse, so

inverse x then -x

1/x-2