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what is inverse function of f (x)=x^2+1 if x>0 and y>1?

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ruals | Salutatorian

Posted August 24, 2013 at 2:47 PM via web

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what is inverse function of f (x)=x^2+1 if x>0 and y>1?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted August 24, 2013 at 3:30 PM (Answer #1)

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You need to evaluate the function inverse, such that:

`{(f(x) = y),(f(x) = x^2 + 1):} => y = x^2 + 1`

You need to write x in terms of y, such that:

`x^2 = y - 1 => x = +-sqrt(y - 1)`

Since the problem provides the information that `x > 0` , yields that `x = sqrt(y - 1).`

You need to interchange the variables, such that:

`y = sqrt(x - 1) => f^(-1)(x) = sqrt(x - 1)`

Hence, evaluating the function inverse, under the given conditions, yields `f^(-1)(x) = sqrt(x - 1).`

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