Let f be an injective map with domain and range such that exactly one of the following statements is correct and the remaining are false The value ofis

The correct answer is:

he domain of the function is {x, y, z}
The range of the function is {1, 2, 3}
The given Statements are



An injective function means the elements of the domain has unique image in the range.
Let’s see the statements one by one
1) f(x) = 1 is true then  are false
f(y) = 1
f(z) = 2
But, the given function is injective. So, f(x) and f(y) cannot have the same image.
Hence, first statement is false.
2) is true. It means  is false.
f(z) = 2
f(x) can be 2 or 3. But 2 is already the image of z.
So, f(x) = 3
f(y) = 1
If we see we get unique image for every element.
Now, we have to find f^-1(1)
f(y) = 1
So, f^-1(1) = y
The right answer is y.

For such questions, we should know concept of injective function.