Set, Relation and FunctionHard
Question
For real x, let f (x) = x3 + 5x + 1, then
Options
A.f is one-one but not onto R
B.f is onto R but not one-one
C.f is one-one and onto R
D.f is neither one-one nor onto R
Solution
Given f(x) = x3 + 5x + 1
Now f′(x) = 3x2 + 5 > 0, ∀x∈R
∴ f(x) is strictly increasing function
∴ It is one-one
Clearly, f(x) is a continuous function and also increasing on R,
Lt f(x) = - ∞ and Lt f(x) = ∞
x → ∞ x → ∞
∴ f(x) takes every value between - ∞ and ∞
Thus, f(x) is onto function.
Now f′(x) = 3x2 + 5 > 0, ∀x∈R
∴ f(x) is strictly increasing function
∴ It is one-one
Clearly, f(x) is a continuous function and also increasing on R,
Lt f(x) = - ∞ and Lt f(x) = ∞
x → ∞ x → ∞
∴ f(x) takes every value between - ∞ and ∞
Thus, f(x) is onto function.
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {x, y) : |x2 - y2| < 16} is given by...Let S be a non-empty subset of R. Consider the following statement: P: There is a rational number x ∈ S such that ...Let R be a relation in N defined by R = {(1 + x, 1 + x2) : x ≤ 5, x ∈ N}. Which of the following is false -...The range of the function f(x) = 7-xPx-3 is...If for three disjoint sets A, B, C; n(A) = 10, n(B) = 6 and n(C) = 5, then n(A ∪ B ∪ C) is equal to -...