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

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 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}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-

If f(x)=(x)/(x-1)=(1)/(y) then the value of f(y)

Find the domain and range of the following f(x)=1/(2x-1)

Find the domain and range of the following f(x)=1/(x^2-1)

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) .