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:{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 {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)

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:{x,y,z}rarr[a,b,c] be a one-one fun and only one of the conditions (i) f(x)!=b, (ii) f(y)=b, (ii) f(2)!=a is true thenthe function fis given by the set

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 A={x:-1 le x le 1}=B be a function f: A to B. Then find the nature of each of the following functions. (i) f(x) = |x| " (ii) " f(x)=x|x| (iii) f(x)=x^(3) " (iv) " f(x)="sin"(pi x)/(2)

If f(x)=sin(pi x), then draw the graph of the followings :(i)y=f(|x|)( ii) y=f(-|x|) (iii) |y|=f(x)

Let f(x) be linear functions with the properties that f(1) le f(2), f(3) ge f(4) " and " f(5)=5. Which one of the following statements is true?