The inverse function is f − 1 ( x + 2 ) = 3 x − 2 2 x + 3 find f ( 1 x − 4 ) .

Question

The inverse function is      f          −      1        (  x  +  2  )  =            3      x      −      2              2      x      +      3      find  f      (          1              x        −        4              )    .

vrtuljakwb · Accepted Answer

Hint: If       f          −      1        (  x  +  2  )  =            3      x      −      2              2      x      +      3      , then       f          −      1        (  x  )  =            3      (      x      −      2      )      −      2              2      (      x      −      2      )      +      3        =            3      x      −      8              2      x      −      1       and you can solve for   f accordingly.

doturitip9 · Accepted Answer

f          −      1        (  x  )  =            3      x      −      8              2      x      −      1        ⇒  y  (  2  x  −  1  )  =  3  x  −  8  ⇒  x  (  2  y  −  3  )  =  y  −  8  ⇒  f  (  x  )  =            x      −      8              2      x      −      3        .So, it follows that:  f      (          1              x        −        4              )    =                    1                  x          −          4                    −      8                      2                  x          −          4                    −      3        =            1      −      8      (      x      −      4      )              2      −      3      (      x      −      4      )        =            8      x      −      33              3      x      −      14

The inverse function is f <mrow class="MJX-TeXAtom-ORD"> −

Answered question

Answer & Explanation

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