Respuesta :

The composition of a function and its inverse is x. So an easy approach to solve this question is to find the composition of a function with itself. If the composition results in an answer "x", then this will mean that function and its inverse are the same.

Finding the composition for 1st option:
[tex](fof)(x) = f(f(x))= \frac{ \frac{x-1}{x+5}-1 }{ \frac{x-1}{x+5}+5 } \\ \\ = \frac{ \frac{x-1-x-5}{x+5} }{ \frac{x-1+5x+25}{x+5} } \\ \\ = \frac{-6}{6x+24} \\ \\ = \frac{1}{x+4} [/tex]

Since the composition of the function with itself is not x, the function and its inverse are not the same.

Similarly, we can find the compositions of next 3 functions with themselves. The results of compositions are listed below:

(gog)(x)=g(g(x)) = x

(hoh)(x)=h(h(x))=[tex] \frac{4x-3}{7-x} [/tex]

(kok)(x)=k(k(x))= x

Thus the option 2 and 4 are the correct answers i.e. these functions are the same as their inverse functions. 

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