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Find the rule for the inverse of the following function:
a) f: [2,∞) -> R, f(x) = sqrt(x-2)

I found the inverse rule to be f-1(x) = x2 + 2

Not sure how the answer got R+ U {0} as the domain. I sketched the equation and the x-intercept point is at 2, so shouldn't it be [2,∞) as the domain?

Thanks

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I think you're getting confused between the original function's domain and the inverse function's domain. The original function's domain is already supplied:

f: [2,∞) -> R, f(x) = sqrt(x-2)

The domain for the inverse function, however, is the range of the original function which is [0,∞)

A useful table, possibly:

Given the original function is f(x), and the inverse function is f-1(x), then:

  • dom f = ran f-1
  • ran f = dom f-1

They swap around, because when you find the inverse, you swap x and y around.

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