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 is a real valued function such that f(x+y) = f(x) + f(y) and f(1)=5, then the value of f(100) 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

The domain of f(x)= (1)/( x^2 +1) is

A function y=f(x) satisfies the differential equation (d y)/(d x)+x^2 y=-2 x, f(1)=1 . The value of |f^( prime prime)(1)| is

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

Find the range of the function f={(1,x),(1,y),(2,x),(2,y),(3,z)}

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]

The domain of f(x) =(1)/(1 -2cosx) is:

Which of the following function from Z to itself are bijections? f(x)=x^3 (b) f(x)=x+2 f(x)=2x+1 (d) f(x)=x^2+x

Find the domain and range of the function f(x)=(x^2)/(1+x^2) . Is the function one-to-one?