Set, Relation and FunctionHard
Question
Let f : (-1, 1) → B, be a function defined by f(x) = tan-1 
, then f is both one-one and onto when B is the interval
, then f is both one-one and onto when B is the intervalOptions
A.
B.
C.
D.
Solution
Given f(x) = tan-1
for x ∈ (-1, 1)
clearly range of f(x) =
∴ co-domain of function = B =
for x ∈ (-1, 1)clearly range of f(x) =
∴ co-domain of function = B =
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
A function f(x) satisfies the relation f(x + y) = f(x) + f(y) + xy (x + y) ∀, x, y, ∈ R. If f′(0) = - ...Let f (x) be a non-negative continuous function such that the area bounded by the curve y = f(x), x-axis and the ordinat...Let ƒ(x) = for all for x ∈ and and g(x) = sin x for all x ∈ Let (ƒog)(x) denotes ƒ(g(x)) and ...Let f : [0, 2] → R be a function which is continuous on [0, 2] and is differentiable on (0, 2) with f(0) = 1. Let ...The relation R in the R of real numbers; defined as R = {(a, b) : a ≤ b2} then R is...