Find f − 1 and verify that ( f x f − 1 ) ( x ) = ( f − 1 x f ) ( x ) = x da x in betwwen da*f* is muliply1.) f ( x ) = x 3 − 1da answer is f − 1 ( x ) = ( x + 1 ) 1 / 3 or x + 1 3 da1/3 is an exponent please explain in detail how to get da answer

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Find       f          −      1       and verify that  (  f  x      f          −      1        )  (  x  )  =  (      f          −      1        x  f  )  (  x  )  =  x da x in betwwen da*f* is muliply1.)  f  (  x  )  =      x          3        −  1da answer is       f          −      1        (  x  )  =  (  x  +  1      )          1            /    3 or             x      +      1        3   da1/3 is an exponent please explain in detail how to get da answer

kunstdansvo · Accepted Answer

To find the inverse of of f(x)Recall that f(x) = y. The equation becomes   y  =      x          3        −  1To begin switch the y with the x and switch the x with the y(in other words the x and y switch). The equation is now:  x  =      y          3        −  1Now, solve for y      y          3        =  x  +  1 (derived by isolating   t  h  e      y          3      )            y              3              3    =            x      +      1        3   To solve for y, we need to get rid of theexponent. Since its cubed, we cube root it. But what you do to oneside, you have to do to the other side, so we also must cube rootthe x+1  y  =            x      +      1        3    y  =  (  x  +  1      )                  1        3             exponent 1/3 meanscube root. The denominator of a fraction exponent  denotes the root,the numerator of the fraction exponent denotes the exponent.       x                  m        n              =            x              m              n  Now write it using inverse notation:      f          −      1        (  x  )  =            x      +      1        3

Trystan Castaneda · Accepted Answer

Find       f          −      1        (  x  ) for   f  (  x  )  =      x          3        −  1To find       f          −      1        (  x  )  :1. Replace f(x) with y.2. Interchange x and y. (This gives the inverse function.)3. Solve for y.4. Replace y with       f          −      1        (  x  ). (This is inverse function notation.)1.  y  =      x          3        −  12.  x  =      y          3        −  13.  x  +  1  =      y          3                  x      +      1        3    =  y  ← cube root each side to solve for y.Also,             y              3              3    =  (      y          3            )          1              /            3        =  y4.       f          −      1        (  x  )  =            x      +      1        3  Prove that   (  f  ∗      f          −      1        )  (  x  )  =  f  (      f          −      1        (  x  )  )  =  x  f  (            x      +      1        3    )  =  (            x      +      1        3        )          3        −  1  =  (  x  +  1  )  −  1  =  x  +  1  −  1  =  xSo it does = x.

Find f^(-1) and verify that (fxf^(-1))(x)=(f^(-1)xf)(x)=x da x in betwwen daf is muliply 1.)f(x)=x^3-1 da answer is f^(-1)(x)=(x+1)^(1/3) or root(3)(x+1) da 1/3 is an exponent please explain in detail how to get daanswer

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