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ConceptInverse of a Function

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#### Question

If the function* f* : R → R be given by *f*[*x*] = *x*^{2} + 2 and *g* : R → R be given by `g(x)=x/(x−1)` , x≠1, find fog and gof and hence find fog (2) and gof (−3).

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test question

Let f : N→N be a function defined as f(x)=9x^{2}+6x−5. Show that f : N→S, where S is the range of f, is invertible. Find the inverse of f and hence find f^{−1}(43) and f^{−1}(163).

#### Reference Material

Solution for concept: Inverse of a Function. For the courses 12th CBSE (Arts), 12th CBSE (Commerce), 12th CBSE (Science)