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  • Which of the following functions from f:A->A are invertible,where x  [-1,1]?<div class='qna-op

Which of the following functions from f:A->A are invertible,where x \epsilon [-1,1]?

Option: 1

f(x)=x/2


Option: 2

g(x) = x


Option: 3

h\left ( x \right )= |x|


Option: 4

k\left ( x \right )= x^{2}


Answers (1)

best_answer

As we learnt

INVERTIBLE FUNCTION 

A function f? X → Y is invertible if and only if f is a bijective function.

 

Now,

Clearly (c) and (d) are ruled out as they are many-one functions.

Also f\left ( x \right )= \frac{x}{2} is one-one but not onto as its range is [-1/2 , 1/2]

g(x) = x is both one-one and onto, hence it is invertible

Posted by

Divya Prakash Singh

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