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Given Function : f(x)= squrt (x-3) Determine the inverse and state is the inverse is a...

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zofic13 | Student, Grade 11 | Salutatorian

Posted July 14, 2011 at 9:04 AM via web

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Given Function :

f(x)= squrt (x-3)

Determine the inverse and state is the inverse is a function.

Please justify your answer.

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rugbykats | High School Teacher | (Level 2) Adjunct Educator

Posted July 14, 2011 at 10:42 AM (Answer #1)

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f(x) = squrt (x-3)

Replace f(x) with y:

y = squrt (x-3)

Replace each y with x and each x with y:

x = squrt (y-3)

Solve for y:

x^2 = y - 3

y = x^2 + 3

Replace the y with f[-1]:

f[-1](x) = x^2 + 3

Since every x value produces a unique y value, it is indeed a function.

Hope this helps. Good luck!

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