Find the inverse f − 1 of f ( x ) = x − 2 . State the domain of f − 1 ( x ). And, check if the inverse function is correct.

Question

Find the inverse       f          −      1       of   f  (  x  )  =      x    −    2  . State the domain of       f          −      1        (  x  ). And, check if the inverse function is correct.

Caiden Li · Accepted Answer

Solution:Consider the function  f  (  x  )  =      x    −    2  Here, the range of x is always a positive value.   (  y  ≥  0  )To find the inverse function ,replace f(x) by x and x by       f          −      1        (  x  ) and simplify it.  x  =            f              −        1              (    x    )    −    2  Squaring both sides to get      x    2    =      f          −      1        (  x  )  −  2or      f          −      1        (  x  )  =      x    2    +  2Hence inverse function is      f          −      1        (  x  )  =      x    2    +  2

Find the inverse f^(-1) of f(x)=sqrt(x-2). State the domain of f(x).

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