The question is: f ( x ) = x x − 1 g ( x ) = 1 x h ( x ) = x 2 − 1Find f ∘ g ∘ h and state its domain.The answer the textbook states is that the domain is all real values of x, except ± 1 and ± 2 .However surely the domain excludes 0 as well, since g ( 0 ) is undefined.

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The question is:  f  (  x  )  =            x              x        −        1              g  (  x  )  =            1      x        h  (  x  )  =      x    2    −  1Find   f  ∘  g  ∘  h and state its domain.The answer the textbook states is that the domain is all real values of   x, except   ±  1 and   ±      2  .However surely the domain excludes   0 as well, since   g  (  0  ) is undefined.

Maleah Lester · Accepted Answer

You&#039;re not inputting   x into   g, though. You&#039;re inputting   h  (  x  ). So yes,   g  (  0  ) is undefined, which means that whatever values of   x makes   h  (  x  )  =  0 is not part of the domain. That&#039;s why they exclude   ±  1.

metal1fc · Accepted Answer

h  (  x  )  =      x    2    −  1 has a value for all   R  g  (  h  (  x  )  )  =      1                  x        2            −      1       which does not have a value at   x  =  ±      1    f  (  g  (  h  (  x  )  )  )  =            1                        x          2                −        1                            1                              x            2                    −          1                    −      1        =      1          1      −              x        2            +      1        =      1          2      −              x        2              which does not have a value at   x  =  ±      2  Hence the total domain is   x  ∈  R  −  {  ±      1    ,  ±      2    }

The question is: f(x)=x/x−1, g(x)=1/x, h(x)=x2−1. Find f o g o h and state its domain.

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