Question
Statement A: An inverse relation is formed when roles of the independent and dependent variables are reversed.
Statement B: If two distinct values in the domain of f have the same image, then the inverse of f is a function.
Which of the above statement(s) is/are true?
- Only A
- Only B
- Both A and B
- Both A and B are false
Hint:
We are given two statements. We have to check if the statements are true or not.
The correct answer is: Only A
The first statement of the given function is true. An inverse relation is formed when roles of independent and dependent variables are reversed.
When we are finding a reverse function we write the independent variable in terms of dependant variable. So, the first statement is true.
The second statement is not true.
The correct statement of B is that if two distinct values in the domain of have the same image, then the inverse of f is not a function.
We cannot find a inverse of a function who has two images. To find a inverse of a function, the function needs to be one-to-one function. A function for which input having two outputs is an invertible function.
The right option is ' only A'.
For such questions, we should know the concept of inverse function.
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