Can anyone help me with this
1 answer:
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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:
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))=
(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.
Finding the composition for 1st option:
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))=
(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.