`f:{x,y,z} to {a,b,c}` is a bijection . It is given that exactly one of the following statements a,b,c, is true and the remaining two are false.
1) `f(x)=a`
2) `f(y) ne a`
3) If `f(z) ne b` then find `f^(-1)(a)`.

Consider that f : A rarr B (i) If f(x) is one-one f(x_(1)) = f(x_(2)) hArr x_(1) = x_(2) or f'(x) ge 0 or f'(x) le 0 . (ii) If f(x) is onto the range of f(x) = B. (iii) If f(x) and g(x) are inverse of each other then f(g(x)) = g(f(x)) = x. Now consider the answer of the following questions. Let f be one-oe function with domain {x, y, z} and range {1, 2, 3}. It is given that exactly one of the following statement is true and the remaining two are false. f(x) = 1, f(y) != 1, f(z) != 2 , then the value of f^(-1)(1) is

Let f be a one-one function with domain {x,y,z} and range {1,2,3}. It is given that exactly one of the following statements is true and the remaining two are false f(X)=1,f(y)!=1f(z)!=2 determine f^(-1)(1)

Let f:{x,y,z}rarr{1,2,3} be a one-one mapping such that only one of the following three statements is true and remaining two are false: f(x)!=2,f(y)=3,f(z)!=1 ,then-

Let f be a one-one function with domain (21,22,23) and range {x,y,z). It is given that exactly one of the following statements is true and the remaining two are false.f(21)=x;f(22);f(23)!=y. Then f^(-1)(x) is

Let f : {x,y, z} to {a, b, c} be a one-one function. If it is known that only one of the following statements is true, (i) f(x)neb (ii) f(y)=b (iii) f(z)nea Determine f^(-1)(b) .

Let f be an injective map.with domain (x,y,z and range (1,2,3), such that exactly one following statements is correct and the remaining are false: f(x)=1,f(y)!=1,f(z)!=2 The value of f^(-1))(1) is

If f(0) = 0 and f(x) =(1)/((1-e^(-1//x))) " for " x ne 0. Then, only one of the following statements on f(x) is true. That is f(x) is