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 (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)!=x ; f(23) != y. Then f^(-1)(x) is

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

Find the domain and range of f(x)=(1)/(2-sin3x).

Let y=f(x) satisfies (dy)/(dx)=(x+y)/(x) and f(e)=e then the value of f(1) is

For y gt 0 and x in R, ydx + y^(2)dy = xdy where y = f(x). If f(1)=1, then the value of f(-3) is

Let f(x) be a linear function which maps [-1, 1] onto [0, 2], then f(x) can be

If f(x) is a linear function and the slope of y=f(x) is (1)/(2) , what is the slope of y = f^(-1)(x) ?

Let f be a real vlaued fuction with domain R such that f(x+1)+f(x-1)=sqrt(2)f(x) for all x in R , then ,

The graph of a function fx) which is defined in [-1, 4] is shown in the adjacent figure. Identify the correct statement(s). (1) domain of f(|x|)-1) is [-5,5] (2) range of f(|x|+1) is [0,2] (3) range of f(-|x|) is [-1,0] (4) domain of f(|x|) is [-3,3]