Set, Relation and FunctionEasy
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.
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